An object of the present invention is to provide a thermoplastic elastomer composition capable of molding a medical tube excellent in the transparency and kink resistance. The present invention is related to a thermoplastic elastomer composition including a hydrogenated block copolymer (A) wherein the copolymer has at least two polymer blocks P composed mainly of an aromatic vinyl compound unit and at least one polymer block Q composed mainly of a conjugated diene compound unit； the total content of aromatic vinyl compound units is from 8 to 25% by mass； and the copolymer contains a high-MFR hydrogenated block copolymer and a propylene polymer (B).
