A linear block copolymer composition having excellent balance between transparency and impact resistance not only in an extrusion molded product and a blow molded product but also in an injection molded product, comprising at least three types of copolymer blocks with different molecular weights in which vinyl aromatic hydrocarbon is used as a monomer unit, wherein the molecular weight distribution of the mixture of the copolymer blocks comes within a specified range. Where a peak top molecular weight corresponding to a peak at which the peak top molecular weight becomes maximum among peaks at which the ratios of the areas thereof to all peak area come within 30% or more in the GPC of the mixture is M1 and a peak top molecular weight corresponding to a peak at which the peak top molecular weight become minimum among the peaks at which peak top molecular weights come within the range of 50,000 or less and the ratios of the areas thereof to all peak areas come within 20% or more in the GPC of the mixture is M2, M1/M2 comes within a specified range.