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

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2006-02-06</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001045609</issuerCik>
        <issuerName>AMB PROPERTY CORP</issuerName>
        <issuerTradingSymbol>AMB</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001213596</rptOwnerCik>
            <rptOwnerName>BAIRD W BLAKE</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O AMB PROPERTY CORPORATION,</rptOwnerStreet1>
            <rptOwnerStreet2>PIER 1, BAY 1</rptOwnerStreet2>
            <rptOwnerCity>SAN FRANCISCO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94111</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>President</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <transactionDate>
                <value>2006-02-06</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>12095</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>51.92</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>272983</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
                <footnoteId id="F2"/>
            </securityTitle>
            <transactionDate>
                <value>2006-02-06</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>40061</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>51.92</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>313044</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Shares were granted pursuant to the Company's 2002 Stock Option and Incentive Plan and are subject to a repurchase right held by AMB Property Corporation, which lapses as to one-third of such shares annually on January 1.  The repurchase right lapses fully on January 1, 2009.</footnote>
        <footnote id="F2">Shares were granted pursuant to the Company's 2002 Stock Option and Incentive Plan and are subject to a repurchase right held by AMB Property Corporation, which lapses as to one-fifth of such shares annually on January 1.  The repurchase right lapses fully on January 1, 2011.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Tamra Browne pursuant to a power or attorney dated 01/12/2003</signatureName>
        <signatureDate>2006-02-08</signatureDate>
    </ownerSignature>
</ownershipDocument>
