UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

SCHEDULE 13D/A

Under the Securities Exchange Act of 1934

(Amendment No. 6)

Red Robin Gourmet Burgers, Inc.

(Name of Issuer)

Common Stock, $0.001 par value

(Title of Class of Securities)

75689M101

(CUSIP Number)

Mr. Jeffrey Blumberg

Drinker Biddle & Reath LLP

191 North Wacker Drive, Suite 3700

Chicago, Illinois 60606

(312) 569-1106

(Name, Address and Telephone Number of Person Authorized to Receive Notices and Communications)

June 13, 2011

(Date of Event which Requires Filing of this Statement)

If the filing person has previously filed a statement on Schedule 13G to report the acquisition which is the subject of this Schedule 13D, and is filing this schedule because of Rule 13d-1(e), 13d-1(f) or 13d-1(g), check the following box  ¨

Note: Schedules filed in paper format shall include a signed original and five copies of the schedule, including all exhibits. See Rule 13d-7 for other parties to whom copies are to be sent.

The information required on the remainder of this cover page shall not be deemed to be “filed” for the purpose of Section 18 of the Securities Exchange Act of 1934 (“Act”) or otherwise subject to the liabilities of that section of the Act but shall be subject to all other provisions of the Act (however, see the Notes).

This Amendment No. 6 to Schedule 13D (this “Schedule 13D” or “Statement”) amends and restates the initial Statement of Beneficial Ownership on Schedule 13D filed with the Securities and Exchange Commission (the “SEC”) on December 10, 2010, as amended by Amendment No. 1 filed with the SEC on December 29, 2010, as amended by Amendment No. 2 filed with the SEC on January 6, 2011, as amended by Amendment No. 3 filed with the SEC on January 24, 2011, as amended by Amendment No. 4 filed with the SEC on March 10, 2011, as amended by Amendment No. 5 filed with the SEC on April 7, 2011, relating to the shares of common stock, $0.001 par value per share (the “Common Stock” or “Shares”) of Red Robin Gourmet Burgers, Inc. (the “Issuer” or “Red Robin”). The Issuer’s principal executive offices are located at 6312 S. Fiddler’s Green Circle, Suite 200N, Greenwood Village, CO 80111.

(a), (b), (c) and (f).

This Schedule 13D is filed by Oak Street Capital SPV 1 LP (“Oak Street SPV”), Oak Street Capital Master Fund, Ltd. (“Oak Street Master”), Oak Street Capital Management, LLC (“Oak Street”), David Makula, and Patrick Walsh (collectively, the “Reporting Persons”). Oak Street SPV and Oak Street Master shall be referred to herein from time to time as the “Funds.”

Oak Street, a Delaware limited liability company, is the general partner of Oak Street SPV, a limited partnership organized under the laws of the State of Delaware. Mr. Makula is the sole Managing Member and Chief Investment Officer of Oak Street. Set forth on Schedule A annexed hereto, is the names and present occupations or employment of the directors of Oak Street Master, a Cayman Island exempted company.

The principal business of Oak Street SPV and Oak Street Master is investing in securities. The principal business of Oak Street is serving as the investment manager of Oak Street SPV, Oak Street Master and various other managed accounts (the “Oak Street Accounts”). Mr. Makula is the sole Managing Member and Chief Investment Officer of Oak Street Capital Management. The principal occupation of Mr. Makula is serving as the sole Managing Member and Chief Investment Officer of Oak Street. The principal occupation of Mr. Walsh is serving as a Senior Partner of Oak Street. Mr. Makula and Mr. Walsh are citizens of the United States of America.

The business address of the Reporting Persons is 111 S. Wacker Drive, 33rd Floor, Chicago, Illinois 60606.

(d) and (e). During the last five years, none of the Reporting Persons have been (i) convicted in a criminal proceeding (excluding traffic violations or similar misdemeanors) or (ii) a party to a civil proceeding of a judicial or administrative body of competent jurisdiction and as a result of such proceeding was or is subject to a judgment, decree or final order enjoining future violations of, or prohibiting or mandating activities subject to, federal or state securities laws or finding any violation with respect to such laws.

The Shares reported in this Schedule 13D as beneficially owned by the Reporting Persons were acquired with funds of approximately $22,246,220 (including brokerage commissions). All such funds were provided from the working capital or personal funds of the Reporting Person who beneficially owns such securities.

The Reporting Persons have acquired or sold the Shares in the ordinary course of business for investment purposes. Shares have been acquired based on their belief that the Shares, when purchased, were undervalued and represented an attractive investment opportunity. The Reporting Persons continually review their respective investments in the Issuer and other entities in which they have invested.

As part of that review, the Reporting Persons determined that they would seek a more active role in influencing the Issuer’s affairs in order to protect and maximize the value of their investments. To that end, Oak Street, on behalf of itself, Oak Street SPV, Oak Street Master, and the Oak Street Accounts, has: engaged in, and, subject to the Letter Agreement (defined below), may continue to engage in, discussions and correspondence with the Issuer’s management and Board of Directors (the “Board”) regarding alternative means to maximize stockholder value; engaged in, and, subject to the Letter Agreement, may continue to engage in, dialogues with other stockholders; and sought, and, subject to the Letter Agreement, may continue to seek, representation on the Board.

Effective as of April 5, 2011, the Issuer, David Makula and Oak Street entered into a Letter Agreement (the “Letter Agreement”) whereby the parties agreed that, among other things, and subject to certain conditions, the Issuer would: (i) appoint Mr. Makula to the Issuer’s Board as a Class I director of the Issuer, effective April 5, 2011, to serve until the Issuer’s 2012 annual stockholders meeting (the “2012 Annual Meeting”); (ii) appoint Mr. Makula to the Audit Committee of the Board (the “Audit Committee”); (iii) increase the size of the Issuer’s Board from 10 to 11 members; and (iv) reimburse the Reporting Persons for certain expenses incurred in connection with their investment in the Issuer. On April 5, 2011, Mr. Makula was appointed as a director of the Board and a member of the Audit Committee. (The Letter Agreement is described in further detail in Item 6 hereof.)

Beginning on June 10, 2011, Oak Street SPV and Oak Street Master effected certain sales to provide additional liquidity to the respective Funds and Fund investors.

Other than as set forth in this Item 4, the Reporting Persons do not have any current plans, proposals or negotiations that relate to or would result in any of the matters referred to in paragraphs (a) through (j) of Item 4 of Schedule 13D. The Reporting Persons intend to review their respective investments in the Issuer on a continuing basis, and to the extent permitted by law and subject to the Letter Agreement, may seek to engage in discussions with other stockholders and/or with management and the Board concerning the business, operations or future plans of the Issuer. Depending on various factors including, without limitation, the Issuer’s financial position, the price levels of the Shares, conditions in the securities markets and general economic and industry conditions, the Reporting Persons may, subject to the Letter Agreement, in the future take such actions with respect to their respective investments in the Issuer as they deem appropriate including, without limitation, purchasing additional Shares, selling of Shares, engaging in short selling of or any hedging or similar transaction with respect to the Shares, taking any other action with respect to the Issuer or any of its securities in any manner permitted by law or changing their intention with respect to any and all matters referred to in paragraphs (a) through (j) of Item 4. The Reporting Persons reserve the right to take whatever future action they deem appropriate regarding the Issuer and its securities under the circumstances as they then exist.

(a), (b) and (c). As of June 20, 2011, the Reporting Persons beneficially owned collectively an aggregate 745,199 Shares, constituting approximately 4.9% of the Shares outstanding (based upon 15,249,589 Shares outstanding, which includes (i) 15,248,756 Shares outstanding on May 18, 2011, as set forth in the Issuer’s Quarterly Report on Form 10-Q as filed with the SEC on May 20, 2011 (the “Issuer Form 10-Q”) and (ii) 833 Shares issuable upon the exercise of stock options awarded to Mr. Makula in connection with his service as a director of the Issuer that are exercisable within 60 days).

As of June 20, 2011, Oak Street SPV beneficially owned 401,409 Shares, constituting approximately 2.6% of the Shares outstanding (the percentage of Shares owned being based upon 15,248,756 Shares outstanding on May 18, 2011, as set forth in the Issuer Form 10-Q).

As of June 20, 2011, Oak Street Master beneficially owned 303,249 Shares, constituting approximately 2.0% of the Shares outstanding (the percentage of Shares owned being based upon 15,248,756 Shares outstanding on May 18, 2011, as set forth in the Issuer Form 10-Q).

As of June 20, 2011, Oak Street indirectly beneficially owned 721,866 Shares, including (i) the 401,409 Shares beneficially owned by Oak Street SPV; (ii) the 303,249 Shares beneficially owned by Oak Street Master; and (iii) 17,208 Shares beneficially owned by the Oak Street Accounts, constituting approximately 4.7% of the Shares outstanding (the percentage of Shares owned being based upon 15,248,756 Shares outstanding on May 18, 2011, as set forth in the Issuer Form 10-Q).

As of June 20, 2011, Mr. Makula beneficially owned 722,699 Shares, including (i) the 721,866 Shares indirectly beneficially owned by Oak Street and (ii) 833 Shares issuable upon the exercise of stock options awarded to Mr. Makula in connection with his service as a director of the Issuer that are exercisable within 60 days (based upon 15,249,589 Shares outstanding, which includes (i) 15,248,756 Shares outstanding on May 18, 2011, as set forth in the Issuer Form 10-Q and (ii) 833 Shares issuable upon the exercise of stock options awarded to Mr. Makula in connection with his service as a director of the Issuer that are exercisable within 60 days).

As of June 20, 2011, Mr. Walsh beneficially owned 22,500 Shares, constituting approximately 0.1% of the Shares outstanding based upon 15,248,756 Shares outstanding on May 18, 2011, as set forth in the Issuer Form 10-Q).

Oak Street is the sole general partner of Oak Street SPV and, accordingly, may be deemed to be the indirect beneficial owner of the Shares that Oak Street SPV beneficially owns. Oak Street, as the sole general partner of Oak Street SPV, has the sole power to direct the voting and disposition of the Shares that Oak Street SPV beneficially owns. Mr. Makula is the sole Managing Member of Oak Street and, accordingly, Mr. Makula may be deemed to be the indirect beneficial owner of the Shares that Oak Street may be deemed to beneficially own.

Oak Street is the sole investment manager of Oak Street Master and, accordingly, may be deemed to be the indirect beneficial owner of the Shares that Oak Street Master beneficially owns. Oak Street, as the sole investment manager of Oak Street Master, has the sole power to direct the voting and disposition of the Shares that Oak Street Master beneficially owns. Mr. Makula is the sole Managing Member of Oak Street and, accordingly, Mr. Makula may be deemed to be the indirect beneficial owner of the Shares that Oak Street may be deemed to beneficially own. Mr. Makula, as the sole Managing Member of Oak Street, has the sole power to direct the disposition of the Shares that Oak Street may be deemed to beneficially own.

Oak Street is the sole investment manager of the Oak Street Accounts and, accordingly, may be deemed to be the indirect beneficial owner of the Shares held in the Oak Street Accounts, none of which beneficially own more than five percent of the outstanding Shares. Oak Street, as the sole investment manager of the Oak Street Accounts, has the sole power to direct the voting and disposition of the Shares held in the Oak Street Accounts. Mr. Makula is the sole Managing Member of Oak Street and, accordingly, Mr. Makula may be deemed to be the indirect beneficial owner of the Shares that Oak Street may be deemed to beneficially own. Mr. Makula, as the sole Managing Member of Oak Street, has the sole power to direct the disposition of the Shares that Oak Street may be deemed to beneficially own.

Mr. Walsh has the sole voting and dispositive power only with respect to the Shares he directly owns.

Beneficial ownership of the Shares shown on the cover pages of and set forth elsewhere in this Schedule 13D for each member of the Reporting Persons assumes that they have not formed a group for purposes of Section 13(d)(3) under the Act, and Rule 13d-5(b)(1) promulgated thereunder. If the Reporting Persons were deemed to have formed a group for purposes of Section 13(d)(3) and Rule 13d-5(b)(1), the group would be deemed to own beneficially (and may be deemed to have shared voting and dispositive power over) 745,199 Shares, constituting approximately 4.9% of the outstanding Shares (the percentage of Shares owned being based upon 15,249,589 Shares outstanding on May 18, 2011, including: (i) 15,248,756 Shares outstanding on May 18, 2011, as set forth in the Issuer Form 10-Q, and (ii) 833 Shares issuable upon the exercise of stock options awarded to Mr. Makula in connection with his service as a director of the Issuer that are exercisable within 60 days).

The filing of this Schedule 13D and any future amendment by the Reporting Persons, and the inclusion of information herein and therein with respect to Oak Street SPV, Oak Street Master, Oak Street and Messrs. Makula and Walsh, shall not be considered an admission that any of such persons, for the purpose of Section 16(b) of the Act, are the beneficial owners of any Shares in which such persons do not have a pecuniary interest. Each of Oak Street SPV, Oak Street Master, Oak Street and Messrs. Makula and Walsh disclaims any beneficial ownership of the Shares covered by this Schedule 13D that he or it does not directly own.

Schedule B annexed hereto lists all transactions in securities of the Issuer during the past 60 days by the Reporting Persons. Unless otherwise indicated, all of such transactions were effected in the open market.

(d) Not applicable.

(e) On June 20, 2011, each of Oak Street Master, Oak Street, and Mr. Makula ceased to be the direct or indirect beneficial owners of more than five percent of the Common Stock, and each such person henceforward will cease to be reporting persons hereunder. To the extent that the Reporting Persons may have been deemed to have formed a group for purposes of Section 13(d)(3) and Rule 13d-5(b)(1) promulgated thereunder, on June 20, 2011, the Reporting Persons collectively ceased to beneficially own more than five percent of the Common Stock in the aggregate, and the Reporting Persons henceforward will cease to be reporting persons hereunder.

Letter Agreement and Appointment of Mr. Makula as Director. Effective as of April 5, 2011, the Issuer, David Makula and Oak Street entered into a Letter Agreement (the “Letter Agreement”) whereby the parties agreed that, subject to certain conditions, the Issuer would: (i) appoint Mr. Makula to the Issuer’s Board as a Class I director of the Issuer, effective April 5, 2011, to serve until the Issuer’s 2012 annual stockholders meeting (the “2012 Annual Meeting”); (ii) appoint Mr. Makula to the Audit Committee of the Board; (iii) increase the size of the Issuer’s Board from 10 to 11 members; and (iv) reimburse the Reporting Persons for certain expenses incurred in connection with their investment in the Issuer. Oak Street also agreed to and withdrew its stockholder nomination letter, dated March 10, 2011, stating its intention to nominate Mr. Makula and Mr. Walsh to the Board. Subject to certain conditions the Reporting Persons, will, among other things: (i) support and vote for the election of certain persons nominated by the Issuer for election to the Board at the 2011 annual stockholders meeting (the “2011 Annual Meeting”); (ii) abstain or vote against any stockholder nominations for directors or other stockholder proposals at the 2011 Annual Meeting; and (iii) support and vote for certain other proposals at the 2011 Annual Meeting.

In addition, subject to certain conditions, the Reporting Persons will, during the period commencing on April 5, 2011 and ending on the date immediately following the day on which the 2012 Annual Meeting is held, or if later, such date that is five months following the latest date on which either Mr. Makula or his replacement ceases to be a director of the Issuer, among other things, refrain from: (i) making or participating in a solicitation of proxies with respect to the voting of any Shares; (ii) initiating any

stockholder proposal; (iii) nominating any candidates for election to the Board; (iv) participating in any “group” with unrelated parties; (v) taking any public action to control or influence the management or policies of the Issuer; (vi) calling a special meeting of the Issuer’s stockholders; (vii) acquiring beneficial ownership of the Issuer’s stock in excess of 16.5% of the then-outstanding Shares; or (viii) publicly seeking a waiver of any of the foregoing. The Issuer and the Reporting Persons will also have certain mutual non-disparagement obligations during such period.

The description of the Letter Agreement in this Statement does not purport to be complete and is qualified in its entirety by reference to the Letter Agreement, a copy of which is filed as Exhibit 99.3 to Amendment No. 5 to the Schedule 13D related to the common stock, $0.001 par value per share, of the Issuer filed April 7, 2011 by the Reporting Persons with the SEC, and is incorporated herein by reference in its entirety.

On April 5, 2011, Mr. Makula was appointed as a director of the Board and a member of the Audit Committee

Director Equity Grants. On April 14, 2011, Mr. Makula received a grant of grant of 397 restricted stock units under the Issuer’s Amended and Restated 2007 Performance Incentive Plan to Mr. Makula. Each restricted stock unit, once vested, will entitle Mr. Makula to receive one Share. The units vest in three substantially equal installments on the first, second and third anniversaries of the date of grant, and the Shares underlying the units will be distributed to Mr. Makula in three substantially equal installments on the third, fourth and fifth anniversaries of the date of grant, unless earlier pursuant to the terms of the award agreement.

On April 14, 2011, Mr. Makula received a grant of options to purchase 5,000 Shares in connection with Mr. Makula’s service as a director of the Issuer. The options vest and become exercisable in equal monthly installments over the 24-month period following the date of grant.

Joint Filing Agreement. Each of the Reporting Persons are a party to a Joint Filing Agreement, dated as of June 24, 2010 (the “13D Joint Filing Agreement”), pursuant to which the parties agreed to jointly file this Schedule 13D and any and all amendments and supplements thereto with the SEC, a copy of which is attached as Exhibit 99.4 to this Statement, and is incorporated herein by reference in its entirety.

Except for the agreements described above, to the best knowledge of the Reporting Persons, there are no contracts, arrangements, understandings or relationships (legal or otherwise) between the Reporting Persons and any other person with respect to any securities of the Issuer including, but not limited to, transfer or voting of any of the securities, finder’s fees, joint ventures, loan or option agreements, puts or calls, guarantees of profits, divisions of profits or loss, or the giving or withholding of proxies.

The following exhibits are filed as exhibits hereto:

SIGNATURE

After reasonable inquiry and to the best of their knowledge and belief, the undersigned certify that the information set forth in this Schedule 13D is true, complete and correct.

SCHEDULE A

Directors of Oak Street Capital Master Fund, Ltd

SCHEDULE B

OAK STREET CAPITAL SPV 1 LP

COMMON STOCK