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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2021-02-18</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001130310</issuerCik>
        <issuerName>CENTERPOINT ENERGY INC</issuerName>
        <issuerTradingSymbol>CNP</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001817841</rptOwnerCik>
            <rptOwnerName>Karuturi Monica</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1111 LOUISIANA</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>HOUSTON</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode></rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>SVP and General Counsel</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2021-02-18</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>11147</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>30857</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Time-based restricted stock units (&quot;RSUs&quot;) awarded under the Issuer's Long-term Incentive Plan (the &quot;Plan&quot;) and vesting (i) in February 2024 if the Reporting Person continues to be an employee of Issuer from the grant date through the vesting date, (ii) in the event of her earlier disability or death, or (iii) on a pro-rata basis upon her earlier retirement unless she satisfies various conditions for full vesting, provided, however, that any such vesting is conditioned upon positive operating income in the last full calendar year of the restricted period except in the case of death or disability.</footnote>
        <footnote id="F2">Total includes (i) 1,395 RSUs previously awarded under the Plan and vesting in February 2021, (ii) 1,243 RSUs previously awarded under the Plan and vesting in February 2022, and (iii) 6,624 RSUs previously awarded under the Plan and vesting in February 2023. The above awards shall vest (i) if the Reporting Person continues to be an employee of Issuer from grant date through vesting date and (ii) in the event of her disability or death.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Vincent A. Mercaldi, Attorney-in-Fact</signatureName>
        <signatureDate>2021-02-22</signatureDate>
    </ownerSignature>
</ownershipDocument>
