The present invention provides a thermoplastic polymer composition mainly comprising a block copolymer prepared by extending, with a specific polyurethane component, the polymer chain of a block copolymer, which may be hydrogenated, having a polymer block of an aromatic vinyl compound and a polymer block of a conjugated diene. The thermoplastic polymer composition according to the present invention is excellent in handling properties and melt-moldability, because it shows non-tackiness. By using the thermoplastic polymer composition according to the present invention, a molded article having high qualities can be produced with good productivity.