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

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2006-08-31</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000005094</issuerCik>
        <issuerName>VAN KAMPEN BOND FUND</issuerName>
        <issuerTradingSymbol>VBF</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001099539</rptOwnerCik>
            <rptOwnerName>CHOATE JERRY D</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>JDC ASSOCIATES</rptOwnerStreet1>
            <rptOwnerStreet2>33971 SELVA RD., SUITE 130</rptOwnerStreet2>
            <rptOwnerCity>DANA POINT</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>92629</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>phantom stock units</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
                <footnoteId id="F2"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2006-08-31</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>633.708</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>17.14</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>1988-08-08</value>
            </exerciseDate>
            <expirationDate>
                <value>1988-08-08</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>common shares</value>
                    <footnoteId id="F1"/>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>633.708</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>16964.482</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The phantom stock units were accrued under the VBF directors' deferred compensation plan and are settled 100% in cash, in generally equal annual installments over a period of five (5) years beginning on the date of the Director's retirement or disability, except that the Board of Directors, in its sole discretion, may accelerate or extend the distribution.</footnote>
        <footnote id="F2">1 for 1</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Jerry D. Choate</signatureName>
        <signatureDate>2006-09-01</signatureDate>
    </ownerSignature>
</ownershipDocument>
