Abstract: Thermoplastic elastomer composition characterized by excellent oil resistance while preserving high tear resistance and tension pull resistance comprises non-functionalized block copolymer of aromatic vinyl compound and conjugated diene or selectively hydrogenated product thereof (e.g. styrene-butadiene-styrene block copolymer), rubber polymer having at least one functional group selected from the group consisting of carboxyl, amino, epoxy and hydroxyl (e.g. acrylonitrile-butadiene copolymer containing a carboxyl group as a reactive functional group), and reactive aromatic vinyl polymer having a functional group which is reactive with the functional group of the rubber (e.g. reactive polystyrene containing 1% by weight oxazolinyl group when the rubber polymer is carboxyl group containing acrylonitrile-butadiene copolymer).