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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-09-27</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001650445</issuerCik>
        <issuerName>Quorum Health Corp</issuerName>
        <issuerTradingSymbol>QHC</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001188873</rptOwnerCik>
            <rptOwnerName>LUMSDAINE ALFRED</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1573 MALLORY LANE</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 100</rptOwnerStreet2>
            <rptOwnerCity>BRENTWOOD</rptOwnerCity>
            <rptOwnerState>TN</rptOwnerState>
            <rptOwnerZipCode>37027</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>EVP &amp; Chief Financial Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common stock, par value $0.0001 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2018-09-27</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>100000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                    <footnoteId id="F1"/>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common stock, par value $0.0001 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2018-09-27</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>100000</value>
                    <footnoteId id="F2"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                    <footnoteId id="F1"/>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>100000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">On September 27, 2018, Quorum Health Corporation (the &quot;Issuer&quot;) and the reporting person entered into an Acknowledgement of Award Cancellation cancelling the March 9, 2018 award of 100,000 shares of the Issuer's restricted common stock because it was issued in excess of the limitations under the Issuer's 2016 Stock Award Plan. Thereafter, the Issuer re-granted to the reporting person 100,000 shares of restricted common stock as an inducement award outside the Issuer's 2016 Stock Award Plan in reliance on the employment inducement exemption to shareholder approval provided under the New York Stock Exchange's Listed Company Manual Rule 303A.08.</footnote>
        <footnote id="F2">50% of the award is time-vested restricted stock and vests in three equal installments beginning on the first anniversary of March 9, 2018, and 50% of the award is performance-based restricted common stock and vests, if at all, over a two-year performance period based on the achievement of target cumulative same store net revenue and target cumulative adjusted EBITDA, each weighted 50%.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ R. Harold McCard, Jr., Attorney in Fact for Alfred Lumsdaine</signatureName>
        <signatureDate>2018-09-28</signatureDate>
    </ownerSignature>
</ownershipDocument>
