<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0304</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2012-02-24</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001171759</issuerCik>
        <issuerName>RED ROBIN GOURMET BURGERS INC</issuerName>
        <issuerTradingSymbol>RRGB</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001349040</rptOwnerCik>
            <rptOwnerName>Menogan Annita M</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>6312 S. FIDDLER'S GREEN CIRCLE</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 200N</rptOwnerStreet2>
            <rptOwnerCity>GREENWOOD VILLAGE</rptOwnerCity>
            <rptOwnerState>CO</rptOwnerState>
            <rptOwnerZipCode>80111</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief Legal Officer</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2012-02-24</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>233</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>34.36</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>17444</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2012-02-27</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>194</value>
                    <footnoteId id="F2"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>34.28</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>17250</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">In connection with the vesting of 750 shares of restricted stock which were granted on February 24, 2009 under the issuer's Amended and Restated 2007 Performance Incentive Plan, the reporting person sold 233 of such shares to the issuer to satisfy her tax withholding obligations.  The sale was approved by the issuer's Compensation Committee in accordance with Rule 16b-3(d)(1) of the Exchange Act (the&quot;Act&quot;), and as such, the sale is exempt from Section 16(b) of the Act pursuant to Rule 16b-3(e) promulgated thereunder.</footnote>
        <footnote id="F2">In connection with the vesting of 625 shares of restricted stock which were granted on February 26, 2008 under the issuer's 2007 Performance Incentive Plan, the reporting person sold 194 of such shares to the issuer to satisfy her tax withholding obligations.  The sale was approved by the issuer's Compensation Committee in accordance with Rule 16b-3(d)(1) of the Act, and as such, the sale is exempt from Section 16(b) of the Act pursuant to Rule 16b-3(e) promulgated thereunder.</footnote>
        <footnote id="F3">Includes 7,632 restricted stock units and 750 shares of restricted stock that are subject to vesting and forfeiture restrictions.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>/s/ Annita M. Menogan</signatureName>
        <signatureDate>2012-02-28</signatureDate>
    </ownerSignature>
</ownershipDocument>
