The crosslinkable rubber composition of the invention is crosslinkable by hot air, and a hot-air crosslinked rubber sheet thereof has no scratch on the surface in a hardness test using a pencil of HB and has a compression set of not more than 70% after a heat treatment at 150.degree. C. for 22 hours. The rubber composition comprises an ethylene/.alpha.-olefin/non-conjugated polyene random copolymer rubber comprising a specific vinyl end group-containing norbornene compound, a SiH group-containing compound having at least two SiH groups in one molecule, and if necessary, an addition reaction catalyst comprising a platinum group element and a reaction inhibitor.