PURPOSE: To produce a high-molecular-weight polymer usable also as a molding material by prepolymerizing a cycloolefin other than cyclohexene by using a specified catalyst and a specified promoter, adding cyclohexene to the reaction mixture, and polymerizing the cyclohexene.

CONSTITUTION: A cycloolefin other than cyclohexene is prepolymerized in the presence of a catalyst component comprising a transition metal catalyst in which the central metal is a metal of any one of groups III-III and an organometallic promoter in which the central metal is a metal of any one of groups II-V, and cyclohexene is added to the reaction mixture and polymerized to obtain a cyclohexene addition polymer comprising repeating units of the formula and having a weight-average molecular weight of 10000 or above (in terms of the molecular weight of the standard polystyrene) as measured by gel permeation chromatography. The obtained cyclohexene addition polymer is a high-molecular-weight one that could not be prepared by prior-art methods and is usable also as a molding material.