PURPOSE: To obtain the composition, comprising a vinyl group-containing organopolysiloxane having the viscosity within a specific range as a base component, having a high tensile strength and elongation and excellent in adhesion to various substrates.

CONSTITUTION: This curable silicone rubber composition is obtained by blending (A) an organopolysiloxane, expressed by formula I [R1 is a monovalent (substituted)hydrocarbon without having an aliphatic unsaturated bond; (m) and (n) are 0 or positive numbers] and having 3000-20000cSt viscosity (at 25°C) with (B) an organopolysiloxane, composed of SiO2 unit, Vi(R2)2SiO0.5 unit and R23SiO0.5 unit (Vi is vinyl; R" is a monovalent hydrocarbon without containing an aliphatic unsaturated bond) and having a resin structure, (C) an organohydrogenpolysiloxane expressed by formula II [R3 is H or the same as R1; R4 is the same as R1; (p) is a positive number; (q) is 0 or a positive number], (D) an isocyanate modified with an organosilane or an organosiloxane and (E) a platinum-based catalyst. The component (B) is blended in an amount of 37-52wt.% based on the total amount of the components (A) and (B).