Strongly acidic cation-exchange membranes were prepared by the electron-beam-induced graft polymerization of glycidyl methacrylate onto a high-density polyethylene film with a thickness of 35 μm and the subsequent conversion of the resulting epoxy group into a sulfonic acid group. The resulting cation-exchange membranes with various ion-exchange capacities or sulfonic acid group densities ranging from 1.9 to 2.7 mmol/g were applied to the enrichment of 0.50 mol/L sulfuric acid by electrodialysis. Concentrated sulfuric acids at concentrations of 1.4 to 2.9 mol/L were obtained in the concentrate chamber during the electrodialysis operated at 30 mA/cm² and 298 K, using a pair of this cation-exchange membrane and a commercially available anion-exchange membrane.