To provide a method for efficiently producing a copolymer of an α-olefin (excluding ethylene) and a cycloolefin having uniform composition and narrow molecular weight distribution.

The α-olefin-cycloolefin copolymer is produced by copolymerizing an α-olefin (excluding ethylene) and a cycloolefin in the presence of a polymerization catalyst containing (a) a transition metal compound expressed by general formula (1) (M is a metallic element of the group 3-10 of the periodic table; R1 and R3 are each a 1-20C hydrocarbon group; R2 and R4 are each H; A1 and A2 are each a bivalent crosslinking group; X is a ligand forming a σ-bond; Y is a Lewis base; (]) is an integer of 1-5; and (r) is an integer of 0-3) and (b) an activation cocatalyst.