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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2019-05-07</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0000275880</issuerCik>
        <issuerName>PARSONS CORP</issuerName>
        <issuerTradingSymbol>PSN</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001699448</rptOwnerCik>
            <rptOwnerName>McMahon Harry T.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>PARSONS CORPORATION</rptOwnerStreet1>
            <rptOwnerStreet2>5875 TRINITY PARKWAY #300</rptOwnerStreet2>
            <rptOwnerCity>CENTREVILLE</rptOwnerCity>
            <rptOwnerState>VA</rptOwnerState>
            <rptOwnerZipCode>20120</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Phantom Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F1"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1940</value>
                    <footnoteId id="F2"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Represents an award granted under the Issuer's Share Value Retirement Plan.  Each share of phantom stock represents a right to receive the cash value of one share of Issuer's common stock.  The phantom stock becomes payable upon the Reporting Person's termination of service as a member of the board of directors in a lump sum or, at the election of the Reporting Person, in a number of monthly installments equal to the number of months for which the Reporting Person received awards of phantom stock under the plan. The phantom stock will be payable in a lump sum upon the death of the Reporting Person or a change in control of Issuer prior to the time all payments in respect of the phantom stock have been paid to the Reporting Person.  The award will be paid in cash. The value of the phantom stock will be determined based on the Issuer's share price at the time of payment.</footnote>
        <footnote id="F2">For the avoidance of doubt, the share number and price per share in this report do not reflect the stock dividend to be effected by Issuer in connection with the closing of the initial public offering.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Michael R. Kolloway, as attorney-in-fact</signatureName>
        <signatureDate>2019-05-07</signatureDate>
    </ownerSignature>
</ownershipDocument>
