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