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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2020-03-18</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001595248</issuerCik>
        <issuerName>Genprex, Inc.</issuerName>
        <issuerTradingSymbol>GNPX</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001807385</rptOwnerCik>
            <rptOwnerName>Wilson William R Jr.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1601 TRINITY STREET</rptOwnerStreet1>
            <rptOwnerStreet2>BLDG B, SUITE 3.322</rptOwnerStreet2>
            <rptOwnerCity>AUSTIN</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>78712</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>2.6700</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2021-03-18</value>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <value>2030-03-17</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>11775</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">(1) One hundred percent (100%) of the shares subject to the option shall vest upon the earlier of (a) the one (1) year anniversary of March 18, 2020 and (b) the day prior to the next annual meeting of Genprex, Inc. stockholders occurring after March 18, 2020, in each case, provided that the optionee continues to serve as a Service Provider (as defined in the Genprex, Inc. 2018 Equity Incentive Plan) through the applicable vesting date.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>/s/ Will R. Wilson Jr.</signatureName>
        <signatureDate>2020-03-20</signatureDate>
    </ownerSignature>
</ownershipDocument>
