To provide a process for producing a norbornene addition polymer by using a new polymerization catalyst which serves to polymerize a norbornene monomer at high activity.

A norbornene monomer is polymerized by using a catalyst comprising a mixture of (A) a compound of a transition metal selected from the group consisting of group 8, group 9 and group 10 metals, (B) a compound containing a halogen atom and an element selected from the group consisting of B, Al, Ti, Zn, Ge, Sn and Sb, and (C) water or an acid the proportions of component A to component B to component C satisfying the relation of the formula: a/4≤c≤4b (wherein a, b and c respectively stand for the numbers of mol of component A, component B and component C).