Abstract: First polymerization of a mixture of styrene-type monomers and conjugated diene monomers containing 30 to 70% by weight of styrene-type monomers is carried out, and when 40 or more of the diene monomers have been converted to a copolymer, there are then added styrene-type monomers in such an amount that the content of styrene units accounts for a proportion of 70 to 85% by weight of the finally obtained block copolymers, followed by completion of the polymerization. Alternatively, when all the diene monomers added have been converted to the copolymer, the second polymerization of styrene type monomers is carried out in the presence of a small amount of conjugated dienes as a polymerization retardant. Block copolymers obtained thus are useful for sheet or film molding having good low-temperature impact strength.