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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-06-03</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001336528</rptOwnerCik>
            <rptOwnerName>Pershing Square Capital Management, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>787 ELEVENTH AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2>9TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10019</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001336477</rptOwnerCik>
            <rptOwnerName>PS Management GP, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>787 ELEVENTH AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2>9TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10019</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001056513</rptOwnerCik>
            <rptOwnerName>ACKMAN WILLIAM A</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>787 ELEVENTH AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2>9TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10019</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common stock, par value $0.01 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2020-06-03</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F4"/>
                <footnoteId id="F5"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1749072</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>58.66</value>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>10448317</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                    <footnoteId id="F6"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common stock, par value $0.01 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2020-06-03</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>C</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F4"/>
                <footnoteId id="F5"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>469691</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>115.00</value>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>10918008</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                    <footnoteId id="F6"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>OTC Equity Forward (call equivalent position)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>115.00</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2020-06-03</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>C</transactionCode>
                <equitySwapInvolved>1</equitySwapInvolved>
                <footnoteId id="F4"/>
                <footnoteId id="F5"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>7</value>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F4"/>
                <footnoteId id="F5"/>
            </exerciseDate>
            <expirationDate>
                <value>2020-06-03</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common stock, par value $0.01 per share</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>4189446</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                    <footnoteId id="F6"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>OTC Put Option (call equivalent position)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>75.08</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2020-06-03</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F4"/>
                <footnoteId id="F5"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>2057000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>17.82</value>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2021-01-06</value>
                <footnoteId id="F4"/>
                <footnoteId id="F5"/>
            </exerciseDate>
            <expirationDate>
                <value>2021-01-06</value>
                <footnoteId id="F4"/>
                <footnoteId id="F5"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common stock, par value $0.01 per share</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>2057000</value>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2057000</value>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                    <footnoteId id="F6"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>OTC Put Option (call equivalent position)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>82.71</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2020-06-03</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F4"/>
                <footnoteId id="F5"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>2057000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>25.70</value>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2021-08-11</value>
                <footnoteId id="F4"/>
                <footnoteId id="F5"/>
            </exerciseDate>
            <expirationDate>
                <value>2021-08-11</value>
                <footnoteId id="F4"/>
                <footnoteId id="F5"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common stock, par value $0.01 per share</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>2057000</value>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2057000</value>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                    <footnoteId id="F6"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>OTC Put Option (call equivalent position)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>79.07</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2020-06-03</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F4"/>
                <footnoteId id="F5"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1405500</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>21.76</value>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2021-01-06</value>
                <footnoteId id="F4"/>
                <footnoteId id="F5"/>
            </exerciseDate>
            <expirationDate>
                <value>2021-01-06</value>
                <footnoteId id="F4"/>
                <footnoteId id="F5"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common stock, par value $0.01 per share</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1405500</value>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1405500</value>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                    <footnoteId id="F6"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>OTC Put Option (call equivalent position)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>91.63</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2020-06-03</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F4"/>
                <footnoteId id="F5"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1405500</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>34.76</value>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2021-08-11</value>
                <footnoteId id="F4"/>
                <footnoteId id="F5"/>
            </exerciseDate>
            <expirationDate>
                <value>2021-08-11</value>
                <footnoteId id="F4"/>
                <footnoteId id="F5"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common stock, par value $0.01 per share</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1405500</value>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1405500</value>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                    <footnoteId id="F6"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">In addition to Pershing Square Capital Management, L.P., a Delaware limited partnership (&quot;Pershing Square&quot;), this Form 4 is being filed jointly by PS Management GP, LLC, a Delaware limited liability company (&quot;PS Management&quot;), and William A. Ackman, a citizen of the United States of America (collectively, the &quot;Reporting Persons&quot;), each of whom has the same business address as Pershing Square and may be deemed to have a pecuniary interest in securities reported on this Form 4 (the &quot;Subject Securities&quot;).</footnote>
        <footnote id="F2">Pershing Square advises the accounts of Pershing Square, L.P., a Delaware limited partnership (&quot;PS&quot;), Pershing Square International, Ltd., a Cayman Islands exempted company (&quot;PS International&quot;), and Pershing Square Holdings, Ltd., a limited liability company incorporated in Guernsey (&quot;PSH&quot; and together with PS and PS International, the &quot;Pershing Square Funds&quot;).</footnote>
        <footnote id="F3">Pershing Square, as the investment adviser to the Pershing Square Funds, may be deemed to be the beneficial owner of the Subject Securities for purposes of Rule 16a-1(a) under the Securities Exchange Act of 1934. As the general partner of Pershing Square, PS Management may be deemed to be the beneficial owner of the Subject Securities for purposes of Rule 16a-1(a). By virtue of Mr. Ackman's position as Chief Executive Officer of Pershing Square and managing member of PS Management, Mr. Ackman may be deemed to be the beneficial owner of the Subject Securities for purposes of Rule 16a-1(a).  Each of the Reporting Persons disclaims any beneficial ownership of any of the Subject Securities, except to the extent of any pecuniary interest therein.</footnote>
        <footnote id="F4">This Form 4 is being filed as a result of the sale of common stock, cash and physical settlement of forward contracts (previously reported on the Form 4 dated December 4, 2019 for transactions as of December 2, 2019), and the sale of over-the-counter European-style put options (&quot;Puts&quot;).  The sale of common stock, cash and physical settlement of forward contracts, and the sale of the Puts were effected at the same time on June 3, 2020.  The sale of the common stock was conducted at the June 3, 2020 market closing price of $58.66 (&quot;Reference Price&quot;); the cash settlement of certain forward contracts was conducted at the same Reference Price (versus the forward price of $115.00); and the Puts were executed based on the same Reference Price.  Further details are set forth Pershing Square's Schedule 13D dated the date of this Form 4.</footnote>
        <footnote id="F5">(Continued from footnote 4) In the case of the physical settlement of certain forwards, the resulting acquisition of common stock was based on the forward price of $115.00 and is exempt from the provisions of Section 16 and the rules promulgated thereunder.  The Puts referred to in Table II do not give the Reporting Persons or the Pershing Square Funds direct or indirect voting, investment or dispositive control over any securities of the Issuer and do not require the counterparties thereto to acquire, hold, vote or dispose of any securities of the Issuer.</footnote>
        <footnote id="F6">Mr. Ackman, a member of the board of directors of the Issuer of the Subject Securities, was elected to that board as a representative of Pershing Square, PS Management, the Pershing Square Funds and Pershing Square GP, LLC.  As a result, each of those entities are directors by deputization for purposes of Section 16 of the Securities Exchange Act of 1934.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Pershing Square Capital Management, L.P., By: PS Management GP, LLC, its General Partner, By: /s/ William A. Ackman, Managing Member</signatureName>
        <signatureDate>2020-06-05</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>PS Management GP, LLC, By: /s/ William A. Ackman, Managing Member</signatureName>
        <signatureDate>2020-06-05</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ William A. Ackman</signatureName>
        <signatureDate>2020-06-05</signatureDate>
    </ownerSignature>
</ownershipDocument>
