A rubber composition is provided, which comprises: (1) 100 parts by mass of a hydrogenated acrylonitrile-butadiene copolymer rubber having high rate of hydrogenation; (2) 1 to 10 parts by mass of an organic peroxide; (3) 0.1 to 15 parts by mass of 2,4-dimercapto-6-substituted-1,3,5-triazine; and (4) 1 to 100 parts by mass of an organic peroxide-crosslinkable polymer having an epoxy group. The rubber composition has high adhesiveness to a metal, high modulus, high set resistance and high heat resistance, thereby being capable of suitably utilizing for composites of rubber and metal, such as belts, tires, rolls, and molded goods, particularly, for composite rubber products of the rubber composition and a brass or bronze-plated steel plate.