An addition curing silicone rubber composition comprising (A) an alkenyl-containing organopolysiloxane, (B) a resinous copolymer composed mainly of R₃SiO_1/2 units and SiO₂ units in a molar ratio between 0.5/1 and 1.5/1 wherein R stands for a monovalent hydrocarbon group and is substantially free of alkenyl groups, (C) a resinous copolymer composed mainly of R₃SiO_1/2 units and SiO₂ units in a molar ratio between 0.5/1 and 1.5/1 wherein R stands for a monovalent hydrocarbon group and includes an alkenyl group, and the total content of alkenyl groups is at least 0.0001 mol/g, (D) an organohydrogenpolysiloxane, and (E) an addition reaction catalyst cures into a silicone rubber sheet that has a satisfactory rubber strength and surface adhesive property.