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

    <schemaVersion>X0303</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2011-06-30</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001498828</issuerCik>
        <issuerName>Howard Hughes Corp</issuerName>
        <issuerTradingSymbol>HHC</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001195979</rptOwnerCik>
            <rptOwnerName>SELLERS R SCOT</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>ONE GALLERIA TOWER</rptOwnerStreet1>
            <rptOwnerStreet2>13355 NOEL ROAD, SUITE 950</rptOwnerStreet2>
            <rptOwnerCity>DALLAS</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75240</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>2011-06-30</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1722</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1722</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Represents restricted stock granted to non-employee directors purusuant to The Howard Hughes Corporation 2010 Equity Incentive Plan.  The shares vest on the earlier of the date of the 2012 annual meeting of stockholders of The Howard Hughes Corporation or June 1, 2012.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Timothy F. Hubach, Attorney-in-Fact for R. Scot Sellers</signatureName>
        <signatureDate>2011-07-05</signatureDate>
    </ownerSignature>
</ownershipDocument>
