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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2017-12-31</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001519758</rptOwnerCik>
            <rptOwnerName>Riley Peter F</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>ONE GALLERIA TOWER,</rptOwnerStreet1>
            <rptOwnerStreet2>13355 NOEL ROAD 22ND FLOOR</rptOwnerStreet2>
            <rptOwnerCity>DALLAS</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75240</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Secretary and General Counsel</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2017-12-31</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1358</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>131.27</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>43614</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Represents shares of common stock withheld by the Issuer to satisfy certain tax withholding obligations upon the vesting of (i) 917 of 1,820 performance-based shares of restricted stock granted in 2013, (ii) 1,820 time-based shares of restricted stock granted in 2013 and (iii) 857 time-based shares of restricted stock granted in 2017. The grant of such restricted stock was previously reported and made under The Howard Hughes Corporation Amended and Restated 2010 Incentive Plan. No shares of common stock were sold by the Issuer or the reporting person.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Timothy F. Hubach, Attorney in Fact for Peter F. Riley</signatureName>
        <signatureDate>2018-01-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
