Thermoplastic polymer composition

A thermoplastic polymer composition comprising

• a thermoplastic polymer (a) having polarity on the main chain of the molecule thereof selected from the group consisting of a polyester and a polyurethane, and
• a modified block copolymer (b) of a block copolymer consisting essentially of units of the structure (B-I)n, (B-I)n-B, [B-(I/B)]n, [B-(I/B)]n-B, wherein n is an integer of 1 to 5, (B-I)-X or [B-(I/B)]-X, wherein X is a 3- to 10-multifunctional coupling agent residue, wherein B represents a polybutadiene block having a degree of vinylization and a degree of unsaturation of not more than 30%, I represents an isoprene block having a degree of vinylization and a degree of unsaturation of not more than 30%, and I/B represents a polymer block obtained by polymerizing a mixture of isoprene and butadiene in a ratio by weight of isoprene/butadiene of 30/70 to 100/0 and hydrogenating the formed polymer block in such a manner that the resulting degree of vinylization and degree of unsaturation is not more than 30%,
• said block copolymer having been subjected to addition reaction with a molecular unit containing a carboxyl acid group or derivative thereof,
• the ratio by weight between said component (a) and said component (b), (a)/(b), being in the range of 2/98 to 98/2.