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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2021-10-07</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001854461</issuerCik>
        <issuerName>Mount Rainier Acquisition Corp.</issuerName>
        <issuerTradingSymbol>RNER</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000318492</rptOwnerCik>
            <rptOwnerName>A.G.P. / ALLIANCE GLOBAL PARTNERS CORP.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>88 POST ROAD WEST</rptOwnerStreet1>
            <rptOwnerStreet2>2ND FLOOR</rptOwnerStreet2>
            <rptOwnerCity>WESTPORT</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06880</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2021-10-07</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>50000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>865000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Transfer of shares pursuant to the Underwriting Agreement, and related agreements, including that certain letter agreement (as amended and restated, the &quot;Side Letter&quot;), by and among the Company, DC Rainier SPV LLC (&quot;Sponsor&quot;), and Reporting Person, as representative of the underwriters (&quot;Representative&quot;) in the Company's initial public offering (&quot;IPO&quot;). As provided in the Side Letter, upon full exercise of the over-allotment option by underwriters in the IPO, Representative agreed to assign and transfer 50,000 shares of common stock to the Company's Sponsor. Such option was exercised in full concurrently with consummation of the Company's IPO on October 7, 2021.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ John Venezia, Chief Compliance Officer</signatureName>
        <signatureDate>2021-10-08</signatureDate>
    </ownerSignature>
</ownershipDocument>
