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

    <schemaVersion>X0508</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2023-11-30</periodOfReport>

    <issuer>
        <issuerCik>0001835597</issuerCik>
        <issuerName>PepGen Inc.</issuerName>
        <issuerTradingSymbol>PEPG</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001763307</rptOwnerCik>
            <rptOwnerName>McArthur James G</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>321 HARRISON AVE., 8TH FLOOR</rptOwnerStreet1>
            <rptOwnerStreet2>C/O PEPGEN INC.</rptOwnerStreet2>
            <rptOwnerCity>BOSTON</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02118</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <officerTitle>President and CEO</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>0</aff10b5One>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2023-11-30</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness></transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1694</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>4.165</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1694</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Shares of Common Stock purchased pursuant to the PepGen Inc. 2022 Employee Stock Purchase Plan (&quot;ESPP&quot;), for the purchase period of June 1, 2023 to November 30, 2023. In accordance with the ESPP, these shares were purchased at a price equal to 85% of the closing price of PepGen's Common Stock on November 30, 2023.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>/s/ Noel Donnelly, as Attorney-in-Fact</signatureName>
        <signatureDate>2023-12-04</signatureDate>
    </ownerSignature>
</ownershipDocument>
