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

    <schemaVersion>X0303</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2010-11-09</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001056513</rptOwnerCik>
            <rptOwnerName>ACKMAN WILLIAM A</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O PERSHING SQUARE CAPITAL MGMT. L.P.</rptOwnerStreet1>
            <rptOwnerStreet2>888 SEVENTH AVENUE, 42ND 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>2010-11-09</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1212309</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>47.62</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3568017</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Warrants</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>50.00</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2010-11-09</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1916667</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F4"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2010-11-09</value>
            </exerciseDate>
            <expirationDate>
                <value>2017-11-09</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common stock, par value $0.01 per share</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1916667</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1916667</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Cash-Settled Total Return Swap</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>36.50</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2010-11-09</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>1</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F5"/>
                    <footnoteId id="F6"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F5"/>
                <footnoteId id="F6"/>
            </exerciseDate>
            <expirationDate>
                <value>2012-08-29</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common stock, par value $0.01 per share</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1146998</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F5"/>
                    <footnoteId id="F6"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Cash-Settled Total Return Swap</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>35.26</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2010-11-09</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>1</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F5"/>
                    <footnoteId id="F6"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F5"/>
                <footnoteId id="F6"/>
            </exerciseDate>
            <expirationDate>
                <value>2015-10-29</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common stock, par value $0.01 per share</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1250836</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F5"/>
                    <footnoteId id="F6"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Cash-Settled Total Return Swap</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>36.08</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2010-11-09</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>1</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F5"/>
                    <footnoteId id="F6"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F5"/>
                <footnoteId id="F6"/>
            </exerciseDate>
            <expirationDate>
                <value>2013-01-31</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common stock, par value $0.01 per share</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1501002</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F5"/>
                    <footnoteId id="F6"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Cash-Settled Total Return Swap</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>38.50</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2010-11-09</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>1</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F5"/>
                    <footnoteId id="F6"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F5"/>
                <footnoteId id="F6"/>
            </exerciseDate>
            <expirationDate>
                <value>2012-11-09</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common stock, par value $0.01 per share</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1501003</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F5"/>
                    <footnoteId id="F6"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Reflects shares of common stock of The Howard Hughes Corporation (the &quot;Company&quot;) purchased pursuant to an investment agreement between General Growth Properties, Inc. (&quot;Old GGP&quot;) and Pershing Square Capital Management, L.P. for the accounts of Pershing Square, L.P., Pershing Square II, L.P. and Pershing Square International, Ltd. (the &quot;Investment Agreement&quot;).  These shares of common stock are held for the accounts of Pershing Square, L.P., Pershing Square II, L.P., and Pershing Square International Ltd. (including shares held for the account of its wholly owned subsidiary, PSRH, Inc.) (collectively, the &quot;Pershing Square Funds&quot;).  PS Management GP, LLC (&quot;PS Management&quot;) is the general partner of Pershing Square Capital Management, L.P. (&quot;Pershing Square&quot;), which acts as investment advisor to the Pershing Square Funds. Pershing Square GP, LLC (&quot;Pershing Square GP&quot;) is the general partner of each of Pershing Square, L.P. and Pershing Square II, L.P. (Continued in footnote 2)</footnote>
        <footnote id="F2">By virtue of his position as managing member of each of PS Management and Pershing Square GP, William A. Ackman may be deemed to be the beneficial owner of the securities listed in Tables I and II.</footnote>
        <footnote id="F3">Includes 2,355,708 shares of common stock of the Company received by the Pershing Square Funds pursuant to the completion of the spin-off of the Company from Old GGP and the distribution of the Company's common stock and the common stock of the reorganized successor to Old GGP (&quot;New GGP&quot;) to holders of Old GGP common stock on November 9, 2010.</footnote>
        <footnote id="F4">Reflects warrants acquired by the Pershing Square Funds pursuant to a warrant agreement, dated as of November 9, 2010, by and among Mellon Investor Services LLC, as warrant agent, and the Company.  The warrants are immediately exercisable from the date of issuance on a net share basis.  The Warrants were acquired by the Pershing Square Funds pursuant to the terms of the Investment Agreement, which included an aggregate equity and debt investment by the Pershing Square Funds of approximately $1.06 billion.</footnote>
        <footnote id="F5">Each of the Pershing Square Funds entered into various cash-settled total return swaps (each a &quot;Swap&quot;) with respect to a notional number of shares of Old GGP common stock prior to the spin-off of the Company from Old GGP.  Immediately following the spin-off and for no additional consideration, each outstanding Swap was converted into a new cash-settled total return swap relating to notional shares of New GGP common stock and a separate cash-settled total return swap relating to notional shares of Company common stock (each an &quot;HHC Swap&quot;). (Continued in footnote 6)</footnote>
        <footnote id="F6">Generally, at the expiration date of each HHC Swap (as set forth in Table II) (i) the applicable Pershing Square Fund is obligated to pay the counterparty, in cash, an amount based on the decrease in price of the Company's shares of common stock from the reference price set forth in Table II, or (ii) the counterparty is obligated to pay the applicable Pershing Square Fund, in cash, an amount based on the increase in price of the Company's shares of common stock from the reference price set forth in Table II.  The HHC Swaps do not give any of Mr. Ackman, the Pershing Square Funds, PS Management, Pershing Square or Pershing Square GP direct or indirect voting, investment or dispositive control over any securities of the Company and do not require the counterparties thereto to acquire, hold, vote or dispose of any securities of the Company.</footnote>
    </footnotes>

    <remarks>Neither the filing of this statement nor anything stated herein shall be deemed an admission that Mr. Ackman is the beneficial owner of any securities covered by the statement.  Mr. Ackman disclaims beneficial ownership of the securities covered by this statement except to the extent of his pecuniary interest therein.</remarks>

    <ownerSignature>
        <signatureName>/s/ William A. Ackman</signatureName>
        <signatureDate>2010-11-12</signatureDate>
    </ownerSignature>
</ownershipDocument>
