The copolymer rubber composition comprises 60 to 75% by weight of a copolymer rubber (1) and 40 to 25% by weight of a copolymer rubber (2), and [iodine value of the copolymer rubber (1)−iodine value of the copolymer rubber (2)] is 5 to 30. The copolymer rubber (1) is an ethylene-α-olefin-nonconjugated polyene copolymer rubber having an ethylene unit of 50 mol % to 70 mol %, an α-olefin unit of 50 mol % to 30 mol %, and an iodine value of 15 to 45, and the copolymer rubber (2) is an ethylene-α-olefinic copolymer rubber having an ethylene unit of more than 70 mol % and 95 mol % or less, an α-olefin unit of less than 30 mol % and 5 mol % or more, and an iodine value of 10 to 30.