PURPOSE: To effect the hydrogenation of a conjugated diene polymer in such a manner that the supported catalyst is easily separated and the catalyst is highly active, by using a specified silica as a carrier in hydrogenating a conjugated polymer with the aid of a supported hydrogenation catalyst.

CONSTITUTION: In hydrogenating a conjugated diene polymer (e.g., acrylonitrile/ butadiene copolymer), there is used, as a carrier to support a gydrogenation catalyst (e.g., a Group VII metal of the periodic table), powder, particulate or molded silica having a specific area ≤600m2/g, pref., ≤500m2/g, an average pore diameter of 80W1,200, pref., 100W1,000, and a particle diameter of 0.015W5mm. The amount of a catalyst metal or nonmetal supported by the silica carrier is usually 0.001W30wt%, pref., 0.01W10wt% based on the carrier. The hydrogenated conjugated diene polymer thus obtained is excellent in resistances to weather, ozone, heat, low temperature and is useful in applications in a wide field.