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

    <schemaVersion>X0303</schemaVersion>

    <documentType>5</documentType>

    <periodOfReport>2010-12-31</periodOfReport>

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    <form3HoldingsReported>0</form3HoldingsReported>

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    <issuer>
        <issuerCik>0001093672</issuerCik>
        <issuerName>PEOPLES BANCORP OF NORTH CAROLINA INC</issuerName>
        <issuerTradingSymbol>PEBK</issuerTradingSymbol>
    </issuer>

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        <reportingOwnerId>
            <rptOwnerCik>0001183128</rptOwnerCik>
            <rptOwnerName>CABLE WILLIAM D</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>518 WEST C STREET</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEWTON</rptOwnerCity>
            <rptOwnerState>NC</rptOwnerState>
            <rptOwnerZipCode>28658</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
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            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>EVP and COO</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

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    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">shares received for 15 Year Service Award</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>William D. Cable, Sr.</signatureName>
        <signatureDate>2011-02-14</signatureDate>
    </ownerSignature>
</ownershipDocument>
