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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4/A</documentType>

    <periodOfReport>2014-05-02</periodOfReport>

    <dateOfOriginalSubmission>2014-07-02</dateOfOriginalSubmission>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000052795</issuerCik>
        <issuerName>ANIXTER INTERNATIONAL INC</issuerName>
        <issuerTradingSymbol>AXE</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001301572</rptOwnerCik>
            <rptOwnerName>Dosch Ted A</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>ANIXTER INTERNATIONAL INC.</rptOwnerStreet1>
            <rptOwnerStreet2>2301 PATRIOT BLVD.</rptOwnerStreet2>
            <rptOwnerCity>GLENVIEW</rptOwnerCity>
            <rptOwnerState>IL</rptOwnerState>
            <rptOwnerZipCode>60026</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Executive VP-Finance &amp; CFO</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common stock</value>
            </securityTitle>
            <transactionDate>
                <value>2014-05-02</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>5</transactionFormType>
                <transactionCode>G</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value>E</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1000</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By wife</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">This amendment is being filed to accurately report that the gift of 1,000 shares previously reported on a voluntary basis on the Form 4 filed July 2, 2014 was made from the common stock indirectly held by the Reporting Person rather than from the common stock directly owned by the Reporting Person, as had been reported.  Accordingly, the amount of securities directly owned by the Reporting Person following the transaction reported on July 1, 2014 is 31,987.  This amount includes 18,755 common stock units.</footnote>
        <footnote id="F2">Shares held by the Ann E. Dosch Trust, the trustee of which is Ann E. Dosch, spouse of the Reporting Person. As such, the Reporting Person is deemed to have beneficial ownership of such shares.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Michele Nelson, by power of attorney</signatureName>
        <signatureDate>2014-07-08</signatureDate>
    </ownerSignature>
</ownershipDocument>
