Abstract: A thermoplastic elastomer composition comprises the following two components:(a) a thermoplastic polyurethane having soft segments from a poly (3-methyl-1,5-pentane adipate) diol having a molecular weight of at least 2,000 and having a JIS A hardness at 25.degree. C. of not more than 80, and(b) a block copolymer comprising at least 2 polymer blocks A principally comprising an aromatic vinyl compound and at least 1 block B comprising an olefinic elastomer, said aromatic vinyl compound being contained in an amount of 5 to 50% by weight based on the weight of the block copolymer and the olefinic elastomer block having a glass transition point of not higher than -20.degree. C. and a heat of fusion of crystal of not more than 8 cal/g;the ratio by weight between the component (a) and the component (b) being (a)/(b)=95/5 to 5/95.