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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2022-03-06</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000004447</issuerCik>
        <issuerName>HESS CORP</issuerName>
        <issuerTradingSymbol>HES</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001453499</rptOwnerCik>
            <rptOwnerName>Hill Gregory P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>HESS CORPORATION</rptOwnerStreet1>
            <rptOwnerStreet2>1185 AVENUE OF THE AMERICAS</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10036</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>COO and President, E&amp;P</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

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            <securityTitle>
                <value>Common Stock, $1.00 par value</value>
            </securityTitle>
            <transactionDate>
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            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>12059</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>130573</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, $1.00 par value</value>
            </securityTitle>
            <transactionDate>
                <value>2022-03-07</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>6725</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>98.39</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
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                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
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                </sharesOwnedFollowingTransaction>
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                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
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            <securityTitle>
                <value>2022 Performance Share Unit</value>
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            <deemedExecutionDate></deemedExecutionDate>
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                <transactionCode>A</transactionCode>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>31940</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
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            <exerciseDate>
                <footnoteId id="F4"/>
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            <expirationDate>
                <footnoteId id="F4"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock, $1.00 par value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>63880</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
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                    <value>31940</value>
                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
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        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Option to purchase Common Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>101.17</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2022-03-06</value>
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            <deemedExecutionDate></deemedExecutionDate>
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                <transactionCode>A</transactionCode>
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            <transactionTimeliness>
                <value></value>
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            <transactionAmounts>
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                    <value>10292</value>
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                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2023-03-06</value>
            </exerciseDate>
            <expirationDate>
                <value>2032-03-06</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock, $1.00 par value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>10292</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
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                <sharesOwnedFollowingTransaction>
                    <value>10292</value>
                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
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        <derivativeTransaction>
            <securityTitle>
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            </conversionOrExercisePrice>
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                <value>2022-03-06</value>
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            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>10293</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2024-03-06</value>
            </exerciseDate>
            <expirationDate>
                <value>2032-03-06</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock, $1.00 par value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>10293</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
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                <sharesOwnedFollowingTransaction>
                    <value>10293</value>
                </sharesOwnedFollowingTransaction>
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                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Option to purchase Common Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>101.17</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2022-03-06</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
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                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>10293</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2025-03-06</value>
            </exerciseDate>
            <expirationDate>
                <value>2032-03-06</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock, $1.00 par value</value>
                </underlyingSecurityTitle>
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                    <value>10293</value>
                </underlyingSecurityShares>
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                    <value>10293</value>
                </sharesOwnedFollowingTransaction>
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                <directOrIndirectOwnership>
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        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Shares sold solely to satisfy tax withholding on vesting of shares of restricted stock.</footnote>
        <footnote id="F2">This amount includes 28,194 shares held in escrow pursuant to the Corporation's Long-Term Incentive Plans. The reporting person has only voting power of these shares until lapsing of the period set by the Committee administering the Plan at which time the shares plus accrued dividends will be delivered to the reporting person if the reporting person is still an employee of the Corporation.</footnote>
        <footnote id="F3">Each Performance Share Unit entitles the holder to a payout of shares of Hess common stock equal to between 0% and 200% of such Performance Share Unit depending on the relative performance of the total shareholder return of Hess common stock compared with that of its peers over a three year performance period ending December 31, 2024, as more particularly described in the applicable award agreement.</footnote>
        <footnote id="F4">Not applicable.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Barry Schachter for Gregory P. Hill</signatureName>
        <signatureDate>2022-03-08</signatureDate>
    </ownerSignature>
</ownershipDocument>
