The present invention is directed to an epoxidized block copolymer composition comprising an epoxidized block copolymer (E) obtained by epoxidizing a block copolymer (C) comprising a polymer block (A) composed mainly of a vinyl aromatic hydrocarbon compound and a polymer block (B) composed mainly of a conjugated diene compound or a product (D) of hydrogenation of the block copolymer (C). The epoxidized block copolymer (E) meets at least one of the following requisites: (1) having a molar ratio (R) of contained hydroxyl to epoxy ranging from 0.001 to 0.1, the molar ratio (R) being represented by the formula: R=[hydroxyl]/[epoxy] (wherein [hydroxyl] represents the amount, in terms of the number of moles, of hydroxyl contained per unit weight of the epoxidized block copolymer and [epoxy] represents the amount, in terms of the number of moles, of epoxy contained per unit weight of the epoxidized block copolymer); (2) having a gel content of not greater than 5% by weight; and (3) having a chloride ion content of not greater than 7 ppm.