A method for producing a block copolymer or hydrogenated product thereof having a polymer block A and a polymer block B, wherein the polymer block A mainly comprises an aromatic vinyl compound unit and the aromatic vinyl compound unit contains a styrene unit in which an alkyl group having at least one functional group selected from a carboxyl group and a group derived therefrom is bound to a benzene ring and the polymer block B mainly comprises a conjugated diene unit, comprising: adding a compound having a carbon-carbon double bond and having at least one functional group selected from a carboxyl group and a group derived therefrom to a block copolymer (I 0) or hydrogenated product thereof having a polymer block A 0 and a polymer block B 0, wherein: the polymer block A 0 comprising an aromatic vinyl compound unit in an amount of 70 % by mass or more, based on the mass of the polymer block A 0, and the aromatic vinyl compound unit containing an alkylstyrene unit in which an alkyl group is bound to a benzene ring; the polymer block B 0 comprising a conjugated diene unit in an amount of 70 % by mass or more, based on the mass of the polymer block B 0; the compound having a carbon-carbon double bond and having at least one functional group being used in an amount of from 2.0 moles to 50 moles based on 1 mole of the block copolymer (I 0), and melt-kneading and reacting the block copolymer (I 0) and the compound having a carbon-carbon double bond and having at least one functional group in a mixer in the presence of a radical initiator at 120 °C to 280 °C, the radical initiator being used in an amount of from 0.001 to 0.25 mole based on 1 mole of the compound having a carbon-carbon double bond and having at least one functional group; wherein the carboxyl group and the group derived therefrom are at least one group selected from the group consisting of a carboxyl group and a salt thereof, an ester group, an amide group, and an acid anhydride group. adding a compound having a carbon-carbon double bond and having at least one functional group selected from a carboxyl group and a group derived therefrom to a block copolymer (I 0) or hydrogenated product thereof having a polymer block A 0 and a polymer block B 0, wherein: the polymer block A 0 comprising an aromatic vinyl compound unit in an amount of 70 % by mass or more, based on the mass of the polymer block A 0, and the aromatic vinyl compound unit containing an alkylstyrene unit in which an alkyl group is bound to a benzene ring; the polymer block B 0 comprising a conjugated diene unit in an amount of 70 % by mass or more, based on the mass of the polymer block B 0; the compound having a carbon-carbon double bond and having at least one functional group being used in an amount of from 2.0 moles to 50 moles based on 1 mole of the block copolymer (I 0), and melt-kneading and reacting the block copolymer (I 0) and the compound having a carbon-carbon double bond and having at least one functional group in a mixer in the presence of a radical initiator at 120 °C to 280 °C, the radical initiator being used in an amount of from 0.001 to 0.25 mole based on 1 mole of the compound having a carbon-carbon double bond and having at least one functional group; the polymer block A 0 comprising an aromatic vinyl compound unit in an amount of 70 % by mass or more, based on the mass of the polymer block A 0, and the aromatic vinyl compound unit containing an alkylstyrene unit in which an alkyl group is bound to a benzene ring; the polymer block B 0 comprising a conjugated diene unit in an amount of 70 % by mass or more, based on the mass of the polymer block B 0; the compound having a carbon-carbon double bond and having at least one functional group being used in an amount of from 2.0 moles to 50 moles based on 1 mole of the block copolymer (I 0), and melt-kneading and reacting the block copolymer (I 0) and the compound having a carbon-carbon double bond and having at least one functional group in a mixer in the presence of a radical initiator at 120 °C to 280 °C, the radical initiator being used in an amount of from 0.001 to 0.25 mole based on 1 mole of the compound having a carbon-carbon double bond and having at least one functional group; wherein the carboxyl group and the group derived therefrom are at least one group selected from the group consisting of a carboxyl group and a salt thereof, an ester group, an amide group, and an acid anhydride group.