NOVELTY - A high gas-permeable cyclic olefin addition polymer is obtained by addition polymerization of cyclic olefin functional siloxane (I), or cyclic olefin functional siloxane (I) and cyclic olefin compound (II). 5-100 Mol.% of structural unit in the addition polymer is derived from the cyclic olefin functional siloxane. The addition polymer has number average molecular weight (in polystyrene conversion) of 10000-2000000 measured by gel permeation chromatography using tetrahydrofuran as a solvent.    USE - High gas-permeable cyclic olefin addition polymer. Uses include but are not limited to film-forming agent for pharmaceutical, foodstuff and cosmetics, oxygen-enriched membrane for air conditioner for motor vehicle, railway, boat and ship, contact lens, fuel cell, aeronautical navigation and semiconductor display device.    ADVANTAGE - The cyclic olefin addition polymer having excellent solubility is efficiently manufactured by simple method. The film formed using the cyclic olefin addition polymer has excellent heat resistance, high gas permeability, thermal stability, mechanical strength and flexibility, and favorable oxygen permeability coefficient and destructive elongation.    DETAILED DESCRIPTION - A high gas-permeable cyclic olefin addition polymer is obtained by addition polymerization of cyclic olefin functional siloxane of formula (I), or cyclic olefin functional siloxane (I) and cyclic olefin compound of formula (II). 5-100 Mol.% of structural unit in the addition polymer is derived from the cyclic olefin functional siloxane. The addition polymer has number average molecular weight (in polystyrene conversion) of 10000-2000000 measured by gel permeation chromatography using tetrahydrofuran as a solvent.    R1=monovalent organic group having aliphatic unsaturated bond;    s=0-2;    i=0 or 1;    j=1-4;    A1-A4=H, halo, 1-10C alkyl, alkenyl, cycloalkyl, aryl, alkoxy, aryloxy, halohydrocarbyl, oxetanyl or alkoxycarbonyl;    or A1+A2+C,A1+A3+C=alicyclic structure, aromatic ring structure, carbonimide or acid anhydride;and    k=0 or 1.    An INDEPENDENT CLAIM is included for manufacture of high gas-permeable cyclic olefin addition polymer, which involves performing addition polymerization of cyclic olefin functional siloxane (I), or cyclic olefin functional siloxane (I), and cyclic olefin compound (II) in presence of multi-component catalyst containing zerovalent palladium compound, ionic boron compound and phosphine compound having substituent chosen from 3-6C alkyl group, cycloalkyl group and aryl group.