A block copolymer composition which is excellent in the balance between transparency and impact resistance and is improved particularly in the impact resistance of products of high-shear injection by inhibiting the products from becoming anisotropic. A block copolymer composition obtained by blending two block copolymers which are each composed of a hard segment block part consisting of a block made mainly from a vinyl aromatic hydrocarbon and a soft segment block part consisting of a block made mainly from a conjugated diene and which are specified in the structure of the hard segment block part. The molded articles made from the composition by not only extrusion or blow molding but also injection are remarkably improved in impact resistance without lowering the transparency.