A process for producing a cycloolefin addition polymer comprising addition-polymerizing a cycloolefin in the presence of a catalyst comprising a combination of a specific transition metal compound of Group 4 of the Periodic Table, with an organoaluminum oxy compound, and/or a compound capable of reacting with the Group 4 transition metal compound to form an ion pair. The specific group 4 transition metal compound preferably has a structure such that the group 4 transition metal is bonded to a cyclopentadienyl ring in an η1 mode. The above-mentioned catalyst exhibits high activity for both of addition homopolymerization of a cycloolefin and addition copolymerization of a cycloolefin with an α-olefin.