PURPOSE: To obtain a catalytic system low in toxity, low in cost, excellent in catalytic activity and capable of polymerizing a cycloolefin, especially, a norbornene deriv. in a large scale by compounding a tungsten compd. with a specific compd. and a boron halide.

CONSTITUTION: A tungsten compd. (A) obtained by combining a tungsten halide and/or a tungsten oxyhalide with a phenol compd. which is substd. with a bulky alkyl group at the positions ortho with respect to the hydroxyl group, a compd. (B) represented by the formula (R1-R3 are each 2-8C substd. alkoxy, H or halogen but at least one of them is H or halogen and an organotin compd. is not contained substantially) (e.g.; triethoxysilane) and boron halide (e.g.; boron tribromide) (C) are compounded so that a molar ratio of the component B: the component A is pref. 6-8 and the molar ratio of the component C: the component A is pref. 3-6 to obtain the objective catalytic system. The component A and cyclic olefin are compounded in a molar ratio of 1:1,000-1:10,000 to perform polymn.