To provide a catalyst for addition polymerization of a cyclic olefin, having excellent addition polymerization activity of the cyclic olefin containing a hydroxy group and/or an acetyl group; to provide a method for producing an addition polymer of the cyclic olefin; and to provide the addition polymer of the cyclic olefin.

A complex of a group 10 transition metal in the periodic table, having a carbene compound as a ligand, preferably the cationic complex represented by general formula (1) is used as the catalyst for the addition polymerization of the cyclic olefin (In the formula, L1 is a carbene compound ligand; L2 is a neutral electron-donating ligand; with the proviso that L1 and L2 may form a polydentate ligand by bonding to each other; and [Y1]- is a monovalent anion).