To provide a method for producing a polymer having an arbitrary molecular weight, with which a cyclic olefin homopolymer and copolymer are readily produced in extremely high catalytic activity, a method for producing a cyclic olefin homopolymer and copolymer having an extremely narrow molecular weight distribution and to obtain an ethylene/norbornene random copolymer having a high norbornene content and high randomness.

The method for producing the cyclic olefin polymer comprises polymerizing a cyclic olefin in the presence of a catalyst obtained by combining (A) a metallocene compound represented by formula (1) (R1, R2 and R3 are each a 1-5C alkyl group and may be the same or different;R4 and R5 are each a 1-3C alkyl group or a halogen and may be the same or different; M is Ti, Zr or Hf) with (B) an alumoxane or a borate or a borane compound.