The present invention presents a novel curable organopolysiloxane composition capable of being adhesively bonded firmly to the surface of various substrates with which it has been in contact during its curing by heating without the primer treatment of the surface. The composition is essentially composed of a diorganopolysiloxane terminated at both chain ends with vinyl groups as the base component, optionally, in combination of a copolymeric organopolysiloxane composed of vinyl-containing monofunctional siloxane units and tetrafunctional siloxane units SiO.sub.2, an organohydrogen-polysiloxane having at least three silicon-bonded hydrogen atoms per molecule as a crosslinking agent by the addition reaction with the vinyl groups in the base component, a platinum catalyst to accelerate the above addition reaction and an alkoxy silane having an aliphatically unsaturated group which serves as a "self-bonding" improver in the composition with or without the addition of a filler.