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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2013-06-25</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001401708</issuerCik>
        <issuerName>NanoString Technologies Inc</issuerName>
        <issuerTradingSymbol>NSTG</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001575799</rptOwnerCik>
            <rptOwnerName>FONSTAD JENNIFER SCOTT</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O DRAPER FISHER JURVETSON</rptOwnerStreet1>
            <rptOwnerStreet2>2882 SAND HILL ROAD, SUITE 150</rptOwnerStreet2>
            <rptOwnerCity>MENLO PARK</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94025</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Series A Preferred Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>364583</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F5"/>
                    <footnoteId id="F6"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Series B Preferred Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F7"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>357144</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F8"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F5"/>
                    <footnoteId id="F6"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Series C Preferred Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F9"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>514916</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F10"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F5"/>
                    <footnoteId id="F6"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Series D Preferred Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F9"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>446504</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F11"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F5"/>
                    <footnoteId id="F6"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Series D Preferred Warrant (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>8.45</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F9"/>
            </exerciseDate>
            <expirationDate>
                <value>2018-11-01</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>89296</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F12"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F5"/>
                    <footnoteId id="F6"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Series E Preferred Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F9"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>81566</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F13"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F5"/>
                    <footnoteId id="F6"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Reflects the automatic conversion of each share of Series A Preferred Stock into 1.4030303030303 shares of Common Stock to occur upon the closing of the Issuer's initial public offering.</footnote>
        <footnote id="F2">Each share has no expiration date.</footnote>
        <footnote id="F3">Reflects a 1-for-32 reverse stock split of the Issuer's outstanding shares effected June 12, 2013.</footnote>
        <footnote id="F4">9,480 of these shares are owned by Draper Associates, L.P., 349,999 of these shares are owned by Draper Fisher Jurvetson Fund VII, L.P., and 5,104 of these shares are owned by Draper Fisher Jurvetson Partners VII, LLC.</footnote>
        <footnote id="F5">Timothy C. Draper, John H.N. Fisher and Steven T. Jurvetson are Managing Directors of the general partner entities of Draper Fisher Jurvetson Fund VII, L.P. (&quot;Fund VII&quot;) that directly hold shares and as such, they may be deemed to have voting and investment power with respect to such shares. Draper Fisher Jurvetson Partners VII, LLC (&quot;Partners VII&quot;) invests lockstep alongside Fund VII. The Managing Partners of Partners VII are Timothy C. Draper, John H.N. Fisher and Steven T. Jurvetson. Draper Associates, L.P. (&quot;DALP&quot;) invests lockstep alongside Fund VII. The General Partners of DALP is Draper Associates, Inc. which is controlled by its President and majority shareholder, Timothy C. Draper. Draper Associates Riskmasters Fund, LLC (&quot;DARF&quot;) and Draper Associates Riskmasters Fund II, LLC (&quot;DARF II&quot;) invest lockstep alongside Fund VII, instead and in place of DALP beginning June 2010. The Managing Member of DARF and DARF II is Timothy C. Draper.</footnote>
        <footnote id="F6">These individuals disclaim beneficial ownership with respect to such shares except to the extent of their pecuniary interest therein.</footnote>
        <footnote id="F7">Reflects the automatic conversion of each share of Series B Preferred Stock into 1.55942857142857 shares of Common Stock to occur upon the closing of the Issuer's initial public offering.</footnote>
        <footnote id="F8">9,286 of these shares are owned by Draper Associates, L.P., 342,857 shares are owned by Draper Fisher Jurvetson Fund VII, L.P., and 5,001 of these shares are owned by Draper Fisher Jurvetson Partners VII, LLC.</footnote>
        <footnote id="F9">Reflects the automatic conversion of each share of Series C Preferred Stock, Series D Preferred Stock and Series E Preferred Stock into one share of Common Stock to occur upon the closing of the Issuer's initial public offering.</footnote>
        <footnote id="F10">13,388 of these shares are owned by Draper Associates, L.P., 494,319 of these shares are owned by Draper Fisher Jurvetson Fund VII, L.P., and 7,209 of these shares are owned by Draper Fisher Jurvetson Partners VII, LLC.</footnote>
        <footnote id="F11">9,621 of these shares are owned by Draper Associates Riskmasters Fund II, LLC, 1,989 of these shares are owned by Draper Associates Riskmasters Fund, LLC, 428,643 of these shares are owned by Draper Fisher Jurvetson Fund VII, L.P., and 6,251 of these shares are owned by Draper Fisher Jurvetson Partners VII, LLC.</footnote>
        <footnote id="F12">396 of these shares are owned by Draper Associates Riskmasters Fund, LLC, 1,923 of these shares are owned by Draper Associates Riskmasters Fund II, LLC, 85,728 of these shares are owned by Draper Fisher Jurvetson Fund VII, L.P., and 1,249 of these share are owned by Draper Fisher Jurvetson Partners VII, L.P.</footnote>
        <footnote id="F13">2,121 of these shares are owned by Draper Associates Riskmasters Fund II, LLC, 78,303 of these shares are owned by Draper Fisher Jurvetson Fund VII, L.P., and 1,142 of these shares are owned by Draper Fisher Jurvetson Partners VII, LLC.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Barbara Mery,
Attorney-in-fact</signatureName>
        <signatureDate>2013-06-25</signatureDate>
    </ownerSignature>
</ownershipDocument>
