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° C. for 22 hours. The rubber composition comprises an ethylene / α-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. The automobile weatherstrip, hose, rubber vibration insulator, belt, sealing material, expanded product, covered electric wire, electric wire joint, electric insulating part and household rubber product according to the invention comprise the above-mentioned rubber composition. The rubber composition has a high crosslinking rate and excellent productivity to produce crosslinked rubber molded products, is capable of undergoing hot-air crosslinking such as HAV or UHF and is capable of providing crosslinked rubber molded products having excellent compression set resistance, strength properties, heat resistance, weathering resistance and abrasion resistance.