Three different cation-exchange membranes with carboxylic acid, phosphoric acid, and sulfonic acid groups, and one anion-exchange membrane with a triethylamine group were prepared by radiation-induced graft polymerization. The maximum capacities of the carboxylic acid, phosphoric acid, sulfonic acid, and triethylamine groups were 3.0, 2.30, 2.43, and 1.42 mmol/g, respectively. The physico-chemical properties of the polyalkene non-woven fabric membrane with four different ion-exchange groups were examined by thermogravimetric analysis, X-ray photoelectron spectrometry (XPS), and scanning electron microscopy. The prepared ion-exchange membrane was applied to the removal of terephthalic acid in dyeing wastewater.