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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-01-29</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001083839</issuerCik>
        <issuerName>Nuveen Quality Municipal Income Fund</issuerName>
        <issuerTradingSymbol>NAD</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000072971</rptOwnerCik>
            <rptOwnerName>WELLS FARGO &amp; COMPANY/MN</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>420 MONTGOMERY STREET</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>SAN FRANCISCO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94163</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000740906</rptOwnerCik>
            <rptOwnerName>WELLS FARGO BANK N A</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>101 NORTH PHILLIPS AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>SIOUX FALLS</rptOwnerCity>
            <rptOwnerState>SD</rptOwnerState>
            <rptOwnerZipCode>57104</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Variable Rate MuniFund Term Preferred Shares, Series 2018</value>
            </securityTitle>
            <transactionDate>
                <value>2018-01-29</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
                <footnoteId id="F2"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>4070</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Subsidiary</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>MuniFund Preferred Shares</value>
            </securityTitle>
            <transactionDate>
                <value>2018-01-29</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
                <footnoteId id="F2"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>6070</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>6070</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Subsidiary</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The disposition of shares occurred pursuant to a Purchase and Exchange Agreement among the Nuveen Quality Municipal Income Fund (the &quot;Issuer&quot;) and Wells Fargo Bank, National Association (the &quot;Bank&quot;) pursuant to which the Bank exchanged 4,070 existing Variable Rate MuniFund Term Preferred Shares, Series 2018, of the Issuer for an equal number of newly issued Series A MuniFund Preferred Shares of the Issuer (&quot;MFP Shares&quot;) and purchased 2,000 newly issued MFP Shares, for a purchase price of $100,000 per share.  The Bank is a wholly owned subsidiary of Wells Fargo &amp; Company (&quot;Wells Fargo&quot;).</footnote>
        <footnote id="F2">This statement is jointly filed by Wells Fargo and the Bank.  Wells Fargo holds an indirect interest in the securities listed in Table I by virtue of its indirect ownership of its subsidiary the Bank.</footnote>
        <footnote id="F3">Each reporting person declares that neither the filing of this statement nor anything herein shall be construed as an admission that such person is, for the purposes of Section 13(d) of the US Securities Exchange Act of 1934 or any other purpose, (i) acting (or has agreed or is agreeing to act together with any other person) as a partnership, limited partnership, syndicate or other group for the purpose of acquiring, holding or disposing of securities of the Issuer or otherwise with respect to the Issuer or any securities of the Issuer or (ii) a member of any group with respect to the Issuer or any securities of the Issuer.</footnote>
    </footnotes>

    <remarks>Exhibits Index
Exhibit 99.1 - Joint Filing Agreement
Exhibit 99.2 - Joint Filer Information</remarks>

    <ownerSignature>
        <signatureName>WELLS FARGO &amp; COMPANY, by: /s/ Lori Ward</signatureName>
        <signatureDate>2018-01-31</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>WELLS FARGO BANK, NATIONAL ASSOCIATION, by: /s/ Adam Joseph</signatureName>
        <signatureDate>2018-01-31</signatureDate>
    </ownerSignature>
</ownershipDocument>
