A method of producing cross-linked rubber including a step of reacting a polyether rubber composition at 130 to 200° C., the polyether rubber composition containing 100 parts by weight of epihalohydrin monomer units, 0.1 to 100 parts by weight of a five-membered ring or six-membered ring nitrogen atom-containing aromatic heterocyclic type compound, and 0.1 to 10 parts by weight of at least one cross-linking agent which is selected from sulfur, a sulfur-containing compound, and triazine-based compound.