Objects of the present invention are to provide a process for easily producing an alkenyl-terminated vinyl polymer without using a metal compound requiring a complicated purification step, and to provide a curable composition containing the vinyl polymer. An alkenyl group is incorporated into an end of a vinyl polymer having a thiocarbonylthio structure at the end to produce an alkenyl-terminated vinyl polymer. Mixing this vinyl polymer with a compound having a hydrogen-silicon bond and a hydrosilylation catalyst gives the curable composition.