A polymer film substrate is irradiated with ions to make a large number of nano-sized through-holes and the substrate is further irradiated with an ionizing radiation so that a functional monomer is grafted or co-grafted onto a surface of the film and within the holes; in addition, the sulfonic acid group is introduced into the graft chains, thereby producing a polymer ion-exchange membrane that has high oxidation resistance, dimensional stability, electrical conductivity and methanol resistance, as well as an ion-exchange capacity controlled over a wide range.