An addition curing silicone rubber composition and a cured product thereof are provided. In this composition, amount of the low molecular weight siloxane component volatilizing from the cured product has been reduced, and as a consequence, this composition is free from the problems such as clouding or haze, contact fault, adhesion failure, and hydrophobicization of the surface caused by the deposition of the volatilized low-molecular weight siloxane component on the surrounding surfaces. More specifically, the addition curing silicone rubber composition comprises; (A) 100 parts by weight of a polyorganosiloxane containing, on average, at least two alkenyl groups which are bonded to silicon atom; (B) 0.3 to 20 parts by weight of an organohydrogenpolysiloxane containing at least two hydrogen atoms which are bonded to silicon atom (SiH functional groups) per molecule; and (C) a catalytic amount of a addition reaction catalyst, and content of the polyorganosiloxane having a degree of polymerization of up to 10 and containing at least one SiH functional group per molecule is up to 0.5% by weight in relation to the entire composition.