To efficiently obtain a cyclic olefin-based polymer of a homopolymer of a cyclic olefin without using a large amount of an organometallic compound by polymerizing specific cyclic olefins in the presence of a specific catalyst.

The objective polymer is obtained by polymerizing (C) cyclic olefins (preferably norbornene or the like) of the formula (R4 to R15 are each H, a 1-20C hydrocarbon or the like; k is ≥0) in the presence of a catalyst comprising (A) a zirconium compound [e.g. tetrakis (2,2,6,6-tetramethyl-3,5- heptanedionate)zirconium or the like] of the formula Zr(RlCOCR2COR3)nX4-n (R1 to R3 are each H or a 1-10C hydrocarbon with proviso that at least one of R1 to R3 is H and the case where all of R1 to R3 are H is omitted; X is a halogen or the like; n is 2 to 4) and (B) a boron compound [preferably triphenylmethyltetrakis(pentafluorophenyl)borate or the like] forming an ionic complex by reacting with a transition metal compound.