To obtain a thermoplastic elastomer composition which has improved softness and compression set and has good low-temperature properties without detriment to its inherent mechanical properties and resistances to heat and oil by compounding a composition containing a thermoplastic copolyester elastomer with a specified amount of a composition containing an acrylic rubber.

A composition containing a thermoplastic copolyester elastomer (A) in an amount of 30-90 pts.wt. is compounded with 10-70 pts.wt. composition containing an acrylic rubber (B). Ingredient A used contains high-melting-point crystalline polymer hard segments containing crystalline aromatic polyester and low-melting-point polymer soft segments containing aliphatic polyester units and/or aromatic polyester units containing aliphatic polyester, and the molar ratio of polyol residues of the hard segments to that of the soft segments is 1/(1.5 or higher but lower than 4.0). Ingredient B used contains at least 25 wt.% units derived from an alkyl acrylate having a 3-18C alkyl group.