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

    <schemaVersion>X0203</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2009-09-15</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001473185</rptOwnerCik>
            <rptOwnerName>MARINER HOLDINGS, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>4200 W. 115TH STREET, SUITE 100</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>LEAWOOD</rptOwnerCity>
            <rptOwnerState>KS</rptOwnerState>
            <rptOwnerZipCode>66211</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>Affiliate of Inv Advisor</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001473713</rptOwnerCik>
            <rptOwnerName>LABEL ARTS, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>PO BOX 727</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>KEMP</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75143</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>Affiliate of Inv Advisor</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001473714</rptOwnerCik>
            <rptOwnerName>WE R, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>631 NORTH 400 WEST</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>SALT LAKE CITY</rptOwnerCity>
            <rptOwnerState>UT</rptOwnerState>
            <rptOwnerZipCode>84103</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>Affiliate of Inv Advisor</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001473509</rptOwnerCik>
            <rptOwnerName>BAW INVESTMENTS, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>316 EAST 31ST STREET</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>KANSAS CITY</rptOwnerCity>
            <rptOwnerState>MO</rptOwnerState>
            <rptOwnerZipCode>64108</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>Affiliate of Inv Advisor</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001473510</rptOwnerCik>
            <rptOwnerName>BICKNELL PROPERTIES, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>4200 W. 115TH STREET, SUITE 100</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>LEAWOOD</rptOwnerCity>
            <rptOwnerState>KS</rptOwnerState>
            <rptOwnerZipCode>66211</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>Affiliate of Inv Advisor</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001473512</rptOwnerCik>
            <rptOwnerName>GREAT PLAINS SANTA RITA, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>4200 W. 115TH STREET, SUITE 100</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>LEAWOOD</rptOwnerCity>
            <rptOwnerState>KS</rptOwnerState>
            <rptOwnerZipCode>66211</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>Affiliate of Inv Advisor</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001473514</rptOwnerCik>
            <rptOwnerName>KCRS PARTNERS, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>4200 W. 115TH STREET, SUITE 100</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>LEAWOOD</rptOwnerCity>
            <rptOwnerState>KS</rptOwnerState>
            <rptOwnerZipCode>66211</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>Affiliate of Inv Advisor</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001418446</rptOwnerCik>
            <rptOwnerName>Bicknell Family Management Company, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>4200 W. 115TH STREET, SUITE 100</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>LEAWOOD</rptOwnerCity>
            <rptOwnerState>KS</rptOwnerState>
            <rptOwnerZipCode>66211</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>Affiliate of Inv Advisor</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001410745</rptOwnerCik>
            <rptOwnerName>Bicknell Family Holding Co LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>4200 W. 115TH STREET, SUITE 100</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>LEAWOOD</rptOwnerCity>
            <rptOwnerState>KS</rptOwnerState>
            <rptOwnerZipCode>66211</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>Affiliate of Inv Advisor</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001473519</rptOwnerCik>
            <rptOwnerName>POWER GROUP COMPANY, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>12721 METCALF AVE., SUITE 103</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>OVERLAND PARK</rptOwnerCity>
            <rptOwnerState>KS</rptOwnerState>
            <rptOwnerZipCode>66213</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>Affiliate of Inv Advisor</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Shares</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes></footnotes>

    <remarks>A form 3 is limited to a maximum of ten reporting persons.  As a result, this Form 3 is one of four filed today reporting the same securities by the following thirty-seven joint filers:  Mariner Holdings, LLC, Mariner Consulting, LLC, Mariner Wealth Advisors, LLC,  Mariner Value Strategies, LLC, Mariner Quantitative Solutions, LLC, MQS Long/Short Equity Fund, L.P., Mariner Real Estate Management, LLC, Mariner Real Estate Partners, LLC, Mariner Anderson One, LLC, Mariner Alternative Asset Management, LLC, Mariner Statistical Opportunities Fund, LP, Mariner Private Equity, LLC, Mariner Capital Ventures, LLC, Tortoise Holdings, LLC, Mariner Insurance Resources, LLC, Mariner Capital Partners, LLC, Mariner Medical Diagnostics 1, LLC, Label Real Estate, LLC, NPC Capital Partners II, LLC, Label Arts, LLC, We R, LLC, BAW Investments, LLC, Bicknell Properties, LLC, Great Plains Santa Rita, LLC, KCRS Partners, LLC, Bicknell Family Management Company, LLC, Bicknell Family Holding Company, LLC, Power Group Company, LLC, Power Group Risk Services, LLC, Adams-Gabbert &amp; Associates, LLC, BF 161 Electric, LLC, BF Wyandotte Development, LLC, Rancho Sienna KC, LP, Trinity Bakersfield Development, LLC, Bicknell Family Finance Company, Santa Rita KC, LLC and Bicknell Family Management Company Trust.</remarks>

    <ownerSignature>
        <signatureName>/s/ S. Kirk Lambright, on behalf of Label Arts, LLC and We R, LLC</signatureName>
        <signatureDate>2009-10-19</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Ryan Anderson, on behalf of BAW Investments, LLC</signatureName>
        <signatureDate>2009-10-19</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Martin C. Bicknell, on behalf of all other reporting persons</signatureName>
        <signatureDate>2009-10-19</signatureDate>
    </ownerSignature>
</ownershipDocument>
