An addition-curable silicone rubber composition comprising: 100 parts by weight of an organopolysiloxane having at least two silicon-bonded C 2 -C 8 alkenyl groups per molecule, an organohydrogenpolysiloxane having at least two silicon-bonded hydrogen atoms per molecule, represented by the following formula: wherein R 1 is a C 1 -C 12 monovalent hydrocarbon group, X is hydrogen or a group R 1, p is an integer of 1 to 50, q is an integer of 1 to 50, meeting 0.1 ≤ p/(p+q) ≤ 1, and at least one X is hydrogen when p is 1, in an amount to give at least 5 moles of silicon-bonded hydrogen atoms in component per mole of alkenyl groups in component, an addition reaction catalyst in an amount to give 1 to 500 ppm of catalyst metal element based on the total weight of components and, 0.1 to 50 parts by weight of finely divided silica having a BET specific surface area of at least 50 m 2 /g, 0.1 to 5.0 parts by weight of a tackifier which is a mixture of (E-1) 1 to 50% by weight of an organohydrogenpolysiloxane having the following formula: wherein R 2 is independently a C 1 -C 12 monovalent hydrocarbon group and r is an integer of 5 to 50, (E-2) 1 to 50% by weight of an alkoxysilyl-modified isocyanurate compound having the following formula: wherein R 3 is independently an allyl group or a group having the following formula: wherein R 4 is a C 1 -C 6 monovalent hydrocarbon group, R 5 is a C 1 -C 4 alkyl group, and x is 2 or 3, and at least two of R 3 are groups of formula, and (E-3) 40 to 90% by weight of an organosilicon compound having at least one epoxy group and at least one alkoxysilyl group per molecule and free of silicon-bonded hydrogen atoms, the total of components (E-1) to (E-3) being 100% by weight, and 0.1 to 5.0 parts by weight of a condensation catalyst comprising at least one organometal compound selected from organotitanium and organozirconium compounds. 100 parts by weight of an organopolysiloxane having at least two silicon-bonded C 2 -C 8 alkenyl groups per molecule, an organohydrogenpolysiloxane having at least two silicon-bonded hydrogen atoms per molecule, represented by the following formula: wherein R 1 is a C 1 -C 12 monovalent hydrocarbon group, X is hydrogen or a group R 1, p is an integer of 1 to 50, q is an integer of 1 to 50, meeting 0.1 ≤ p/(p+q) ≤ 1, and at least one X is hydrogen when p is 1, in an amount to give at least 5 moles of silicon-bonded hydrogen atoms in component per mole of alkenyl groups in component, an addition reaction catalyst in an amount to give 1 to 500 ppm of catalyst metal element based on the total weight of components and, 0.1 to 50 parts by weight of finely divided silica having a BET specific surface area of at least 50 m 2 /g, 0.1 to 5.0 parts by weight of a tackifier which is a mixture of (E-1) 1 to 50% by weight of an organohydrogenpolysiloxane having the following formula: wherein R 2 is independently a C 1 -C 12 monovalent hydrocarbon group and r is an integer of 5 to 50, (E-2) 1 to 50% by weight of an alkoxysilyl-modified isocyanurate compound having the following formula: wherein R 3 is independently an allyl group or a group having the following formula: wherein R 4 is a C 1 -C 6 monovalent hydrocarbon group, R 5 is a C 1 -C 4 alkyl group, and x is 2 or 3, and at least two of R 3 are groups of formula, and (E-3) 40 to 90% by weight of an organosilicon compound having at least one epoxy group and at least one alkoxysilyl group per molecule and free of silicon-bonded hydrogen atoms, the total of components (E-1) to (E-3) being 100% by weight, and (E-1) 1 to 50% by weight of an organohydrogenpolysiloxane having the following formula: wherein R 2 is independently a C 1 -C 12 monovalent hydrocarbon group and r is an integer of 5 to 50, (E-2) 1 to 50% by weight of an alkoxysilyl-modified isocyanurate compound having the following formula: wherein R 3 is independently an allyl group or a group having the following formula: wherein R 4 is a C 1 -C 6 monovalent hydrocarbon group, R 5 is a C 1 -C 4 alkyl group, and x is 2 or 3, and at least two of R 3 are groups of formula, and (E-3) 40 to 90% by weight of an organosilicon compound having at least one epoxy group and at least one alkoxysilyl group per molecule and free of silicon-bonded hydrogen atoms, the total of components (E-1) to (E-3) being 100% by weight, and 0.1 to 5.0 parts by weight of a condensation catalyst comprising at least one organometal compound selected from organotitanium and organozirconium compounds.