The objective of the invention is to solve the problems of conventional polymer electrolyte membranes, including small ion-exchange capacity and low oxidation and methanol resistance. A polymer film substrate is irradiated with γ-rays, electron beams or other radiations to perform multi-graft polymerization with functional monomers and then the polymer film substrate containing the grafted molecular chains or the graft molecular chains into which sulfonic acid groups have been introduced is crosslinked by irradiation to produce a polymer electrolyte membrane that has outstanding oxidation resistance, dimensional stability, electrical conductivity and methanol resistance and which can be controlled in ion-exchange capacity over a wide range.