The present invention relates to a method for producing a vinyl polymer retaining the ability for atom transfer radical polymerization, a method for reliably producing a vinyl polymer having terminal functional groups, a vinyl polymer having functional groups prepared by these methods, and a curable composition comprising the polymer. A vinyl polymer having terminal functional groups can be reliably produced through the steps of preparing a vinyl polymer by atom transfer radical polymerization of a vinyl monomer in a polymerization solvent in the presence of a polymerization initiator and a transition metal complex functioning as a polymerization catalyst, removing the polymerization solvent and the vinyl monomer while the ability for atom transfer radical polymerization is maintained, and supplying a functional-group-introducing agent having a low polymerizability to introduce a functional group to a polymer terminus. During the step of supplying the functional-group-introducing agent, a functional-group-introducing solvent having a dielectric constant higher than that of the functional-group-introducing agent may be supplied to effectively introduce a functional group to a terminus of the vinyl polymer. Furthermore, according to the present invention, the polymerization solvent and the functional-group-introducing agent can be recovered and recycled.