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

    <schemaVersion>X0306</schemaVersion>

    <documentType>5</documentType>

    <periodOfReport>2018-05-31</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <form3HoldingsReported>1</form3HoldingsReported>

    <form4TransactionsReported>1</form4TransactionsReported>

    <issuer>
        <issuerCik>0001268533</issuerCik>
        <issuerName>TORTOISE ENERGY INFRASTRUCTURE CORP</issuerName>
        <issuerTradingSymbol>TYG</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000813913</rptOwnerCik>
            <rptOwnerName>KNIGHTS OF COLUMBUS</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1 COLUMBUS PLAZA</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW HAVEN</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06510</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Preferred Stock 4.01%</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <transactionCoding>
                <transactionFormType>3</transactionFormType>
            </transactionCoding>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>5000000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Preferred Stock 4.34%</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <transactionCoding>
                <transactionFormType>3</transactionFormType>
            </transactionCoding>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>15000000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Preferred Stock 4.01%</value>
            </securityTitle>
            <transactionDate>
                <value>2014-12-17</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value>L</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>300000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>10.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>8000000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Preferred Stock 4.34%</value>
            </securityTitle>
            <transactionDate>
                <value>2014-12-17</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value>L</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>600000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>10.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>21000000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Knights of Columbus became a beneficial owner of these securities as of October 9, 2014, which made Knights of Columbus subject to Section 16 as a 10% holder based upon 22,400,000 shares of mandatory redeemable preferred (MRP) stock outstanding as of November 30, 2014, as set forth in the issuer's financial statements contained in its annual report to shareholders for the period ended November 30, 2014, as filed with the Securities and Exchange Commission on January 21, 2015.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Gilles Marchand, Vice President</signatureName>
        <signatureDate>2018-10-10</signatureDate>
    </ownerSignature>
</ownershipDocument>
