A curable organopolysiloxane composition comprising:(A) an organopolysiloxane having at least two aliphatic unsaturated hydrocarbon groups,(B) a particular organohydrogenpolysiloxane having a group represented by the formula: ##STR1## wherein R.sup.3 is a substituted or unsubstituted monovalent hydrocarbon group and a is an integer of 2 or 3, and(C) a platinum catalyst.This composition has good curing properties, and the silicone film obtained by curing has good release properties which is stable for a long period of time.