To provide a method for producing an α-olefin-cycloolefin copolymer having high molecular weight and broad molecular weight distribution, keeping excellent polymerization activity especially even in a non-aromatic solvent without lowering the molecular weight in high production efficiency.

The α-olefin-cycloolefin copolymer is produced by copolymerizing an α-olefin and a cycloolefin in the presence of a polymerization catalyst composed of a polycrosslinked metallocene compound (a-1) expressed by general formula (I), a metallocene compound (a-2) different from the compound (a-1) and an activation cocatalyst (b) and, as necessary, an organic aluminum compound (c).