The object of the present invention is to produce a polymer, which is free from the troubles of the coloration and the decrease in the mechanical properties of molded articles (films, etc.), crosslinkage failure, migration (stain) or the like, by the living radical polymerization method wherein the content of impurities consisting of a transition metal and its ligand employed as a polymerization activator is reduced. A process for producing a polymer is described, comprising: a) the step of performing a polymerization reaction by using a monomer, a transition metal and its ligand and a polymerization initiator to form a polymer; and b) the step of eliminating the transition metal and its ligand contained in the polymer under the condition of a viscosity of 100 Pa.multidot.s or below, wherein the step b comprises: b1) the former step of eliminating the transition metal and its ligand insoluble in the polymer; and b2) the latter step of eliminating the transition metal and its ligand dissolved in the polymer.