To obtain a polymer well-soluble in a halogen type satd. hydrocarbon by polymerizing a norbornene type monomer in the presence of a specific polymerization catalyst.

A norbornene type monomer is polymerized in the presence of a polymerization catalyst obtd. by reacting a halide of at least one type of transition metal selected from the group consisting of groups VIII, IX and X metals of the periodic table with a compd. comprising a metallic element selected from the group consisting of B, Al, Ti, Zn, Ge, Sn and Sb atoms without a carbon which directly binds to the metallic element, at -30 to 150°C for 1 min to 100 hr to obtain the objective norbornene addn. polymer having a repeating unit of the formula (wherein R1-R8 are each H, a 1-3C hydrocarbon group or a halogen; R9-R12 H, a 1-20C hydrocarbon group, a halogen or a substituent contg. Si, O or N in which R8 and R11 may be combined to form a ring; and (n) is 0-2) with a number average mol.wt. (gel permeation chromatography, polystyrene converted) to 10,000-1,000,000 and 0.1 wt.% or less of a matter insol. in chloroform.