To a heat-curable silicone rubber composition comprising (a) an organopolysiloxane having at least two alkenyl groups in a molecule, (b) an organohydrogenpolysiloxane having at least two hydrogen atoms in a molecule, and (c) a platinum catalyst is added (d) ammonia or an ammonia precursor so that ammonia or ammonia precursor is present in an amount of 10 to 500 parts by weight of nitrogen per million parts by weight of the total of components (a), (b) and (c) in a cured product of the heat-curable silicone rubber composition. The composition cures into a silicone rubber having minimized compression set without a need for secondary vulcanization.