To obtain an α-olefin/cycloolefin copolymer having a narrow molecular weight distribution and a process for producing the copolymer with high polymerization activity.

The α-olefin/cycloolefin copolymer is obtained by copolymerizing a 2-30C α-olefin with at least one cycloolefin selected from cycloolefins (I), (II) and (III), each having a specified structure, in the presence of a metallocene compound represented by formula (IV) and a cocatalyst comprising e.g. an organoaluminum oxy compound. The copolymer has an Mw/Mn of 1.2 to 4.0, an [η] of 0.01 to 20, and a ratio of α-olefin/cycloolefin of 99/1 to 20/80.