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

    <schemaVersion>X0303</schemaVersion>

    <documentType>4/A</documentType>

    <periodOfReport>2010-05-27</periodOfReport>

    <dateOfOriginalSubmission>2010-06-01</dateOfOriginalSubmission>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000879575</issuerCik>
        <issuerName>TERRA NITROGEN CO L P /DE</issuerName>
        <issuerTradingSymbol>TNH</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001234192</rptOwnerCik>
            <rptOwnerName>LLOYD ANNE H</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>4 PARKWAY NORTH</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 400</rptOwnerStreet2>
            <rptOwnerCity>DEERFIELD</rptOwnerCity>
            <rptOwnerState>IL</rptOwnerState>
            <rptOwnerZipCode>60015-2950</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Phantom Units</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2010-05-27</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>17.08</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>73.40</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Phantom Units</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>17.08</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1019.79</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">This amendment on Form 4/A is being filed to clarify which phantom units the reporting person has elected to defer upon vesting.</footnote>
        <footnote id="F2">The phantom units represent cash distribution equivalents pursuant to the compensation plan for outside directors.  The phantom units vest and are settled in cash on January 15th of each year, unless deferred at the reporting person's option and subject to the reporting person's continued service as a director at the time of vesting.  Vested deferred phantom units are settled in cash after the reporting person ceases to be a director of the issuer.  The reporting person has elected to defer 8.54 of the phantom units reported hereon upon vesting.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Debra J. Bliven, by Power of Attorney for Anne H. Lloyd</signatureName>
        <signatureDate>2010-06-24</signatureDate>
    </ownerSignature>
</ownershipDocument>
