There is provided a curable organopolysiloxane composition comprising (A) an organopolysiloxane containing, in its molecule, at least two groups represented by the general formula (1): CH.sub.2 .dbd.CH--(CH.sub.2).sub.a --(OC.sub.b H.sub.2b).sub.c --O--(1) wherein a is an integer of 1 to 8, b is an integer of 2 to 4, and c is an integer of 0 to 3; (B) an organohydrogenpolysiloxane containing, in its molecule, at least two hydrogen atoms each bonded to a silicon atom; (C) an addition-reaction retarder; and (D) a platinum family metal catalyst. The composition is fast in curing speed and superior in curing stability.