<?xml version="1.0"?>

<ownershipDocument>

    <schemaVersion>X0201</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2003-12-31</periodOfReport>


    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001027258</issuerCik>
        <issuerName>SOUTHWEST BANCORP OF TEXAS INC</issuerName>
        <issuerTradingSymbol>SWBT</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001224921</rptOwnerCik>
            <rptOwnerName>ANDREAS DALE H</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O SOUTHWEST BANCORPORATION OF TEXAS</rptOwnerStreet1>
            <rptOwnerStreet2>4400 POST OAK PARKWAY</rptOwnerStreet2>
            <rptOwnerCity>HOUSTON</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>77027</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>President/Mitchell Mortgage</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>

        <nonDerivativeTransaction>
            <securityTitle>
                <value>Restricted Stock, $1.00 par value</value>
            </securityTitle>
            <transactionDate>
                <value>2003-12-31</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>588</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>38.895</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4775</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>

    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">This transaction was made under SEC Rule 10b5-1.</footnote>
    </footnotes>

    <remarks>Exhibit 24 attached.</remarks>

    <ownerSignature>
        <signatureName>/s/Loretta Riggsby, attorney-in-fact</signatureName>
        <signatureDate>2004-01-05</signatureDate>
    </ownerSignature>

</ownershipDocument>

