An olefin thermoplastic elastomer composition comprising 10 to less than 60 parts by weight of a crystalline polyolefin resin (A) and 90 to more than 40 parts by weight of an ethylene/ alpha -olefin/nonconjugated polyene copolymer rubber (B), the total amount of components (A) and (B) being 100 parts by weight, said rubber (B) being obtainable by random copolymerization of ethylene, an alpha -olefin having 3 to 20 carbon atoms and a nonconjugated polyene in the presence of a metallocene catalyst and having: (1) a molar ratio of (a) units derived from ethylene to (b) units derived from the alpha -olefin having 3 to 20 carbon atoms of 40:60 to 95:5 ((a):(b)); (2) an iodine value of 1 to 50; and (3) an intrinsic viscosity ( eta ), as measured in decalin at 135 DEG , of 0.1 dl/g to 10 dl/g.