An addition-curable silicone rubber composition which contains: 100 parts by weight of (A) an organopolysiloxane that is represented by average composition formula (1) R1aSiO(4−a)/2 (wherein R1 represent monovalent hydrocarbon groups that are the same as or different from each other, and a represents a positive number of 1.5-2.8) and has at least two alkenyl groups, each of which is bonded to a silicon atom, in each molecule; 0.3-20 parts by weight of (B) an organohydrogen polysiloxane that has at least two hydrogen atoms (SiH functional groups), each of which is bonded to a silicon atom, in each molecule; 5-80 parts by weight of (C) a reinforcing silica; and (D) an addition reaction catalyst, which is configured of a platinum group metal, in an amount of 0.5-1,000 ppm relative to the total weight of the components (A) and (B). This addition-curable silicone rubber composition also contains (E) an organopolysiloxane, which has one or more Si—OH functional groups in each molecule, while having a polymerization degree of 10 or less, in an amount of 0.005-0.3% by weight relative to the total weight of the composition.