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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-07-21</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001290149</issuerCik>
        <issuerName>ProNAi Therapeutics Inc</issuerName>
        <issuerTradingSymbol>DNAI</issuerTradingSymbol>
    </issuer>

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        <reportingOwnerId>
            <rptOwnerCik>0001305641</rptOwnerCik>
            <rptOwnerName>Parfet Donald R</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O PRONAI THERAPEUTICS, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>2150 ? 885 WEST GEORGIA ST.</rptOwnerStreet2>
            <rptOwnerCity>VANCOUVER</rptOwnerCity>
            <rptOwnerState>A1</rptOwnerState>
            <rptOwnerZipCode>V6C 3E8</rptOwnerZipCode>
            <rptOwnerStateDescription>BRITISH COLUMBIA, CANADA</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
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            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chairman of the Board</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

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            <securityTitle>
                <value>Series C Preferred Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F5"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2015-07-21</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>C</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>13130</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F5"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F5"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F5"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>13130</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Palmero Group LLC</value>
                    <footnoteId id="F12"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Each share of the issuer's Series A Preferred Stock automatically converted into 1.12593 shares of the issuer's Common Stock on July 21, 2015 in connection with the closing of the issuer's sale of its Common Stock in its firm commitment initial public offering (the &quot;IPO&quot;) pursuant to a registration statement on Form S-1 (File No. 333-204921) under the Securities Act of 1933, as amended (the &quot;Registration Statement&quot;), and had no expiration date.</footnote>
        <footnote id="F2">The reporting person is the managing member of Apjohn Group, LLC (&quot;AG LLC&quot;), and has sole voting and dispositive power over the shares held by Apjohn Group, LLC.  The reporting person disclaims beneficial ownership over such securities except to the extent of his pecuniary interest therein, and the inclusion of these securities in this report shall not be deemed an admission of beneficial ownership of the reported securities for purposes of Section 16 or for any other purposes.</footnote>
        <footnote id="F3">Each share of the issuer's Series B-1 Preferred Stock automatically converted into 1 share of the issuer's Common Stock on July 21, 2015 in connection with the closing of the issuer's sale of its Common Stock in its IPO pursuant to the Registration Statement, and had no expiration date.</footnote>
        <footnote id="F4">The reporting person is a managing member of Apjohn Ventures, LLC (&quot;AV LLC&quot;), which is the general partner of Apjohn Ventures Annex Fund LP (&quot;AVAF&quot;), the record holder of the securities, and may be deemed to share voting and dispositive power over the securities held by AVAF.  The reporting person disclaims beneficial ownership over such securities except to the extent of his pecuniary interest therein, and the inclusion of these securities in this report shall not be deemed an admission of beneficial ownership of the reported securities for purposes of Section 16 or for any other purposes.</footnote>
        <footnote id="F5">Each share of the issuer's Series C Preferred Stock automatically converted into 1 share of the issuer's Common Stock on July 21, 2015 in connection with the closing of the issuer's sale of its Common Stock in its IPO pursuant to the Registration Statement, and had no expiration date.</footnote>
        <footnote id="F6">Each share of the issuer's Series D Preferred Stock automatically converted into 1 share of the issuer's Common Stock on July 21, 2015 in connection with the closing of the issuer's sale of its Common Stock in its IPO pursuant to the Registration Statement, and had no expiration date.</footnote>
        <footnote id="F7">Represents shares of Common Stock issued by the issuer in payment of cumulative accrued dividends.</footnote>
        <footnote id="F8">The reporting person is a managing member of AV LLC, which is the general partner of Apjohn Ventures Fund, LP (&quot;AVF&quot;), the record holder of the securities, and may be deemed to share voting and dispositive power over the securities held by AVF.  The reporting person disclaims beneficial ownership of such securities except to the extent of his pecuniary interest therein, and the inclusion of these securities in this report shall not be deemed an admission of beneficial ownership of the reported securities for purposes of Section 16 or for any other purposes.</footnote>
        <footnote id="F9">Each share of the issuer's Series B Preferred Stock automatically converted into 1.11111 shares of the issuer's Common Stock on July 21, 2015 in connection with the closing of the issuer's sale of its Common Stock in its IPO pursuant to the Registration Statement, and had no expiration date.</footnote>
        <footnote id="F10">The reporting person's wife is the trustee of the Ann VanDeWater Parfet 2006 Revocable Trust, Dated May 5, 2006.  The reporting person disclaims beneficial ownership of such securities, and the inclusion of these securities in this report shall not be deemed an admission of beneficial ownership of the reported securities for purposes of Section 16 or for any other purposes.</footnote>
        <footnote id="F11">The reporting person is the trustee of the Donald R. Parfet 2006 Trust, Dated May 1, 2006.</footnote>
        <footnote id="F12">The reporting person is a managing member of Palmero Group LLC, and has sole voting and shared dispositive power over the shares held by Palmero Group LLC.  The reporting person disclaims beneficial ownership over such securities except to the extent of his pecuniary interest therein, and the inclusion of these securities in this report shall not be deemed an admission of beneficial ownership of the reported securities for purposes of Section 16 or for any other purposes.</footnote>
        <footnote id="F13">The warrant is exercisable at any time at the holder's election on a one-for one basis and automatically terminates on the completion of the issuer's initial public offering if not earlier exercised.</footnote>
        <footnote id="F14">The warrant has a net exercise provision under which the holder, in lieu of paying the exercise price in cash, can surrender the warrant and receive a net number of shares of preferred stock based on the fair market value of such stock at the time of exercise, after deducting the aggregate exercise price.</footnote>
        <footnote id="F15">Represents the number of shares that were withheld by the issuer in satisfaction of the exercise price of the warrants listed in Table II and does not represent a sale of securities by the reporting person.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Sukhi Jagpal as attorney-in-fact for Donald Parfet</signatureName>
        <signatureDate>2015-07-21</signatureDate>
    </ownerSignature>
</ownershipDocument>
