A cross-linked rubber exhibits high strength and excellent abrasion resistance as compared with a known cross-linked rubber. The cross-linked rubber is obtained by cross-linking a rubber composition that includes a hydrogenated conjugated diene-based polymer, an olefin-based rubber, and a cross-linking agent, the hydrogenated conjugated diene-based polymer being a hydrogenated product of a polymer that includes a structural unit derived from butadiene, and including at least one of an amino group and a hydrocarbyloxysilyl group at one terminal or each terminal.