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

    <schemaVersion>X0508</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2024-07-18</periodOfReport>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001923040</rptOwnerCik>
            <rptOwnerName>Mellion Michelle L</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>
            <isOfficer>1</isOfficer>
            <officerTitle>Chief Medical Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>1</aff10b5One>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2024-07-18</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness></transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>12625</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>10.21</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>12625</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2024-07-18</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness></transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>12625</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>18.2023</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>10.21</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2024-07-18</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness></transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>12625</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <value>2032-06-30</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>12625</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>57772</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The transactions reported in this Form 4 were effected pursuant to a Rule 10b5-1 trading plan adopted by the reporting person on January 19, 2024.</footnote>
        <footnote id="F2">The price reported in Column 4 is a weighted average price. These shares were sold in multiple transactions at prices ranging from $18.00 to $18.56, inclusive. The reporting person undertakes to provide to the Issuer, any security holder of the Issuer, or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of shares sold at each separate price within the range set forth in this footnote.</footnote>
        <footnote id="F3">This option shall vest as follows: twenty-five percent (25%) on the one-year anniversary of the Grant Date and the remainder vesting in thirty-six (36) equal monthly installments, subject to the option recipient's continued service or employment with the Company on each applicable vesting date.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>/s/ Noel Donnelly, as Attorney-in-Fact</signatureName>
        <signatureDate>2024-07-19</signatureDate>
    </ownerSignature>
</ownershipDocument>
