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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2021-04-29</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001840317</issuerCik>
        <issuerName>Plum Acquisition Corp. I</issuerName>
        <issuerTradingSymbol>PLMI</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001190699</rptOwnerCik>
            <rptOwnerName>BURNS URSULA M</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O PLUM ACQUISITION CORP. I</rptOwnerStreet1>
            <rptOwnerStreet2>2021 FILLMORE ST. #2089</rptOwnerStreet2>
            <rptOwnerCity>SAN FRANCISCO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94115</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Executive Chairwoman</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Class B ordinary shares</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2021-04-29</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>644591</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A ordinary shares</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>644591</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>7980409</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F3"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Plum Partners, LLC</value>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">This Form 4 reflects the automatic surrender to the issuer of 644,591 of the issuer's Class B ordinary shares, par value $0.0001 per share, for no consideration byPlum Partners, LLC (the &quot;Sponsor&quot;) pursuant to contractual arrangements with the issuer, triggered by the expiration of the option of the underwriter of the issuer's initial public offering to purchase additional units.</footnote>
        <footnote id="F2">As described in the issuer's registration statement on Form S-1 (File No. 333-253331) under the heading &quot;Description of Securities -- Founder Shares&quot;, the Class B ordinary shares will automatically convert into Class A ordinary shares, par value $0.0001 per share, of the issuer at the time of the issuer's initial business combination, or earlier at the option of the holder, on a one-for-one basis, subject to adjustment for share subdivisions, share capitalizations, reorganizations, recapitalizations and the like, and certain anti-dilution rights and have no expiration date.</footnote>
        <footnote id="F3">The securities reported herein are held directly by the Sponsor. The reporting person controls the Sponsor, and as such, has voting and investment discretion with respect to the securities held by the Sponsor and may be deemed to have beneficial ownership of the securities held directly by the Sponsor. The reporting person disclaims beneficial ownership of the securities reported hereby except to the extent of her pecuniary interest therein, and the inclusion of these securities in this report shall not be deemed an admission of beneficial ownership of all of the reported securities for purposes of Section 16 or for any other purposes.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Kanishka Roy as attorney-in-fact for Ursula Burns</signatureName>
        <signatureDate>2021-05-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
