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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-04-30</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001534992</issuerCik>
        <issuerName>Fiesta Restaurant Group, Inc.</issuerName>
        <issuerTradingSymbol>FRGI</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001275002</rptOwnerCik>
            <rptOwnerName>FRIEDMAN BRIAN P</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O JEFFERIES FINANCIAL GROUP INC.</rptOwnerStreet1>
            <rptOwnerStreet2>520 MADISON AVENUE</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10022</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $0.01 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2019-04-30</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>5925</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                    <footnoteId id="F1"/>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>45767</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock, par value $0.01 per share</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>28668</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The Shares were granted to the Reporting Person pursuant to the Issuer's 2012 Stock Incentive Plan and subject to restrictions on transfer. The stock award reported herein shall vest (and the restrictions shall lapse) in full on the earlier of (i) one business day before the Issuer's 2020 annual meeting of stockholders or (ii) April 30, 2020, provided that in each case the Reporting Person has continuously remained a director of the Issuer. Any unvested shares underlying the stock award reported herein will be immediately forfeited upon the Reporting Person ceasing to be a director. The stock award reported herein is not transferable unless vested.</footnote>
        <footnote id="F2">The Reporting Person is the general partner of 2055 Partners L.P. (&quot;2055 Partners&quot;) and, in such capacity, may be deemed to beneficially own the 28,668 shares of common stock of the Issuer beneficially owned by 2055 Partners.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Brian P. Friedman</signatureName>
        <signatureDate>2019-05-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
