PURPOSE: To obtain polynorbornene in a high yield by polymerizing a cycloolefin in the presence of a specific metallocene compound and a promoter.

CONSTITUTION: A ligand obtained by bonding (substituted) cyclopentadienyl groups or substituted derivatives thereof through C, Si, Ge, etc., is coordinated to a halide of Ti, Zr, Hf, etc. The coordination compound is hydrogenated at the indenyl or hafnium groups to obtain a metallocene compound comprising the hydrogenated groups bonded to each other. A 5C or higher cycloolefin is polymerized at ordinary pressure to 50kg/cm2 and 0 to 200°C in the presence of a catalyst comprising the above compound and a promoter.