A thermoplastic elastomeric composition which have an improved compression set and good electrical properties is provided.The disclosed is thermoplastic elastomeric composition which includes 0.1-30 parts by weight of carbon fibrous structures per 100 parts by weight of a thermoplastic elastomer, wherein the carbon fibrous structure comprises a three dimensional network of carbon fibers each having an outside diameter of 15-100 nm, wherein the carbon fibrous structure further comprises a granular part with which the carbon fibers are tied together in the state that the concerned carbon fibers are externally elongated therefrom, and wherein the granular part is produced in a growth process of the carbon fibers.