NOVELTY - A metal ion chosen from group IV transition metal element, group V transition metal ion and platinum ion or gold ion is added to primary suspension liquid. The solid-liquid separation process of primary suspension liquid is performed, and the obtained solid phase is again dispersed in solvent to obtain secondary suspension liquid. The metal particles are added to the secondary suspension liquid, to obtain metal particles-supported catalyst dispersion liquid, and then dried to obtain metal particles-supported catalyst.    USE - Manufacture of metal particles-supported catalyst used for hydrogenation of unsaturated hydrocarbon, aromatic, ester, aldehyde, or ketones, oxidation of alcohol, methylene, diesel motor vehicle waste gas, or gasoline-automobile waste gas, dehydrogenation of gasoline, saturated hydrocarbon, unsaturated hydrocarbon, or aromatics, and hydrocracking of gasoline, benzoyl group derivatives, epoxy derivatives, nitric acid, or sulfuric acids (all claimed).    ADVANTAGE - The method provides metal particles-supported catalyst having excellent catalytic activity, durability and dispersibility.    DETAILED DESCRIPTION - A metal ion (0.1-100 parts mass) chosen from group IV transition metal element, group V transition metal ion and platinum ion or gold ion is added to primary suspension liquid obtained by dispersing support substance containing ion exchanger in solvent. The solid-liquid separation process of primary suspension liquid is performed, and the obtained solid phase is again dispersed into a solvent to obtain secondary suspension liquid. The metal ion which is not supported by the support substance is removed. The metal particles (0.01-50 parts mass) having average particle diameter of 1-20 nm chosen from group IV transition metal element, group V transition metal element, and palladium particles or gold particles are added to the secondary suspension liquid at 15-40 degrees C, to obtain metal particles-supported catalyst dispersion liquid. The obtained metal particles-supported catalyst dispersion liquid is dried at 100-200 degrees C, to obtain metal particles-supported catalyst.