The present invention provides an acrylic block copolymer composition improving melt flowability at molding and being excellent in heat resistance in addition to keep weather resistance, chemical resistance, adhesion property, flexibility and abrasion resistance which are the characteristics of the acrylic block copolymer. It is attained by a thermoplastic elastomer composition comprising an acrylic block copolymer (A) which comprises a methacrylic polymer block (a) and an acrylic polymer block (b), wherein at least one of polymer blocks among the methacrylic polymer block (a) and the acrylic polymer block (b) has an acid anhydride group and/or a carboxyl group, and an acrylic polymer (B) having 1.1 or more of epoxy groups in one molecule.