Disclosed is a thermoplastic elastomer composition obtained by dynamically crosslinking a composition composed of a component (A), a component (B) and a component (C) with 0.05 to 5 parts by mass of a crosslinking agent per 100 parts by mass of the component (A). The component (A) is 50 to 85 parts by mass of an acrylic rubber prepared by copolymerizing a monomer mixture mainly containing an alkyl acrylate and also containing 0.5 to 15% by mass of an epoxy group-containing monomer. The component (B) is 15 to 50 parts by mass of a thermoplastic polyester resin. The component (C) is 1 to 35 parts by mass of a graft copolymer or a precursor thereof per 100 parts by mass of the total of the components (A) and (B), and the graft copolymer is composed of an olefin polymer segment and a vinyl copolymer segment.