A cross-linked rubber is excellent in both fuel oil resistance and cold resistance. A cross-linkable rubber composition contains: a nitrile group-containing copolymer rubber [A] including less than 30 wt % α,β-ethylenically unsaturated nitrile monomer units (a1), conjugated diene monomer units (b1), and α,β-ethylenically unsaturated dicarboxylic acid monoester monomer units (d1), wherein at least part of the conjugated diene monomer units (b1) is hydrogenated; a nitrile group-containing copolymer rubber [B] including not less than 30 wt % α,β-ethylenically unsaturated nitrile monomer units (a2) and conjugated diene monomer units (b2), wherein at least part of the conjugated diene monomer units (b2) may be hydrogenated; and an amine-based cross-linking agent.