NOVELTY - Thermoplastic polymer composition comprises block copolymer mixture (a), polyvinyl acetate having a acetalization degree (b) and thermoplastic elastomer (c). The block copolymer mixture comprises hydrogenated copolymer (a1) containing at least one polymer block (A1) which comprises aromatic vinyl units and at least one polymer block (B1) containing hydrogenated conjugated diene units, and hydrogenated block copolymer (a2) comprising at least one polymer block (A2).    USE - The thermoplastic polymer composition is useful for molded product (claimed), as covering materials including component of electronic apparatus, electronic office equipment, household appliances, motor vehicles, large sized display, portable telephone apparatus, digital still camera, portable radio cassette reproduction machine, and inverter, and as impact relieving material, gasket, sealing material of glass, corrosion resistant material, connection portion of the glass, metal frames in window, and separator of secondary battery for variety-of-information terminal devices, such as a notebook personal computer, mobile telephone, video camera, hybrid vehicle, and fuel cell electric vehicle.    ADVANTAGE - The composition has excellent flexibility, dynamics characteristic, moldability, color protection property, adhesiveness. The covering material has anti-slip function, waterproof property, and excellent design.    DETAILED DESCRIPTION - Thermoplastic polymer composition comprises (in parts mass): block copolymer mixture (a) (100), polyvinyl acetate (0.1-100) having a acetalization degree of 55-88 mol% (b) and thermoplastic elastomer (c) (0.1-20). The block copolymer mixture comprises hydrogenated copolymer (a1) containing at least one polymer block (A1) (5-40 %mass or less) which comprises aromatic vinyl units, and at least one polymer block (B1) containing hydrogenated conjugated diene units, and hydrogenated block copolymer (a2) comprising at least one polymer block (A2) (40-70 %mass or less) which comprises aromatic vinyl units and at least one polymer block (B2) containing hydrogenated conjugated diene units. The thermoplastic elastomer comprises at least one polymer block (A3) containing aromatic vinyl units, at least one polymer block (B3) containing hydrogenated conjugated diene units and at least one polymer block (C) containing polar functional group. An INDEPENDENT CLAIM is included for molded product which comprises the above-mentioned composition.