Provided is a curable silicone rubber composition, including: (A) an organopolysiloxane containing two or more silicon atom-bonded aliphatic unsaturated groups within each molecule, and containing a phenyl group and/or cyclohexyl group, (B) an organopolysiloxane resin with a three dimensional network structure consisting essentially of Q units and M units, and containing one or more phenyl groups and/or cyclohexyl groups, (C) an organohydrogenpolysiloxane, and (D) a platinum group metal-based catalyst, in which the component (B) exists in a quantity that represents from 20 to 80% by mass of the combination of the component (A) and the component (B), and in the component B, the quantity of low molecular weight substances, for which the weight average molecular weight measured by GPC and calculated against polystyrene standards is not greater than 500, is not greater than 5%. The composition is capable of forming a cured product with improved hardness, no surface tackiness, a high refractive index, and excellent resistance to thermal shock, without any loss in rubber-like properties such as elongation.