The curable composition provided by the present invention comprises a butadiene polymer having organosilicon groups as the pendant groups, an ethylenically unsaturated polymerizable compound, an organic peroxide, and optionally a filler. The butadiene polymer being the base of this composition can readily be obtained by the platinum-catalyzed addition reaction between an organosilicon compound having a hydrogen atom directly bonded to the silicon atom in a molecule and the ethylenic unsaturation of a conventional butadiene polymer.The compositions of the invention are remarkably superior in many respects to those composition based on ordinary butadiene polymers, and useful for applications in a wide variety including the production of electrically insulating materials and various kinds of industrial articles.