NOVELTY - A cyclic olefin addition polymer is obtained by addition-polymerizing cyclic olefin functional siloxane (I) and cyclic olefin compound (II), or cyclic olefin functional siloxane (I) in presence of multi-component catalyst containing ( beta )-diketone palladium compound (A), ionic boron compound (B) and phosphine compound (C) having substituents chosen from 3-6C alkyl group, cycloalkyl group and aryl group. The number average molecular weight of cyclic olefin addition polymer is 200000-1500000, measured by gas permeation chromatography based on polystyrene conversion.    USE - Cyclic olefin addition polymer. Uses include but are not limited to oxygen-enriched membrane for air-conditioner, fuel cell, contact lens, residence, motor vehicles, pharmaceuticals, foodstuff and cosmetics.    ADVANTAGE - The cyclic olefin addition polymer has excellent gas permeability, oxygen permeability, thermal stability, mechanical strength, and film forming property.    DETAILED DESCRIPTION - A cyclic olefin addition polymer is obtained by addition-polymerizing cyclic olefin functional siloxane of formula (I) and cyclic olefin compound of formula (II), or cyclic olefin functional siloxane (I) in presence of multi-component catalyst containing ( beta )-diketone palladium compound (A), ionic boron compound (B) and phosphine compound (C) having substituents chosen from 3-6C alkyl group, cycloalkyl group and aryl group. The ratio of structural unit originating in cyclic olefin functional siloxane (I) is 40-100 mol%. The number average molecular weight of cyclic olefin addition polymer is 200000-1500000, measured by gas permeation chromatography based on polystyrene conversion.    R1=monovalent organic group which does not contain aliphatic unsaturated bond;    s=0-2;    j=0 or 1;    A1-A4=H, halo, 1-10C alkyl, alkylene, cycloalkyl, aryl, alkoxy, aryloxy, halogenated hydrocarbyl, alkoxycarbonyl or oxetanyl;    A1+A2,A1+A3=optionally alicyclic structure, aromatic ring, carbonimide or acid-anhydride group;and    i=0 or 1.    An INDEPENDENT CLAIM is included for manufacture of cyclic olefin addition polymer.