An olefin thermoplastic elastomer composition comprises a crystalline polyolefin resin (A) and an ethylene/&agr;-olefin/nonconjugated polyene copolymer rubber (B), and optionally a softener (C) and/or an inorganic filler (D), in a specific ratio. The copolymer rubber (B) is prepared by the use of a metallocene catalyst and comprises ethylene, an &agr;-olefin of 3 to 20 carbon atoms and a nonconjugated polyene. This composition ca provide molded products of more excellent tensile strength, elongation at break, elastomeric properties (elongation set, permanent compression set, etc.), heat resistance and low-temperature properties than the conventional non-crosslinked olefin thermoplastic elastomers, even if the composition is in the non-crosslinked form. The composition in the partially or completely crosslinked form can provided molded products of more excellent low-temperature properties, tensile strength, elongation at break and elastomeric properties than the conventional vulcanized rubbers.