PURPOSE: To obtain a polymer blend having material characteristics of strength, hardness, heat resistance, and toughness especially by mixing a fine grain polyolefin, a fine grain cycloolefin polymer and a specific block copolymer to be heated and shearing-processed.

CONSTITUTION: (A) A fine grain cycloolefin polymer (favorably, fine grain aliphatic poly-l-olefin) in an amount of 0-95 pts.wt., (B) 0-95 pts.wt. of a fine grain polyolefin (favorably, polyethylene) and (C) 0.1-99 pts.wt. of a block polymer obtained by polymerizing one or more kinds of monomers of formulae I VI (R1-R8 are each H, a 1-8C alkyl), 0-95 wt.% of a cycloolefin of formula VII ((n) is 2-10) per the total amount of monomers, and 0-99 wt.% of a cycloolefin of formula VIII (R9-R12 are the same as R1) per the total amount of monomers at -78 to 150°C under a pressure of 0.01-64 bar and in the presence of a catalyst (molecular weight distribution MW/Mn is less than 2, monomer/comonomer ratio is changed by 10% or more, and other reaction conditions are changed) as an additive are mixed, heated and shearing-processed to obtain 100 pts.wt. of the objective blend.