Provided is a curable silicone rubber composition, comprising (A) an organopolysiloxane containing two or more aliphatic unsaturated bonds within each molecule, having a viscosity at 25° C. within a range from 10 to 100,000 mm2/s, and containing a phenyl group and/or cyclohexyl group, (B) an organopolysiloxane with a resin structure comprising SiO2 units and (R1)3SiO0.5 units (wherein, each R1 represents, independently, a vinyl group, an allyl group, or a monovalent hydrocarbon group that contains no aliphatic unsaturated bonds, provided one or more of all the R1 groups within this component (B) represent, independently, a phenyl group or a cyclohexyl group), (C) an organohydrogenpolysiloxane, and (D) a platinum group metal-based catalyst, wherein 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). The composition is capable of forming a cured product with improved hardness, no surface tackiness, and a high refractive index, without any loss in rubber-like properties such as elongation. A substrate such as an electrical or electronic component or an optoelectronic component can be coated with the cured product by applying the composition to the substrate and curing the composition to form the cured product on top of the substrate.