Poly(hexafluoropropylene-co-tetrafluoroethylene) (FEP) was successfully radiation-grafted with vinylbenzyl chloride (VBC). Subsequently amination with trimethylamine followed by ion exchange with aqueous hydroxide yielded alkaline anion-exchange membranes (AAEMs). Experimental parameters were established for maximising the degree of grafting (d.o.g.); the optimum treatment duration for maximum amination was also established. The graft penetration at different degrees of grafting was investigated and related to the grafting conditions. The stabilities of the grafted membranes and the final AAEMs were thoroughly investigated using thermogravimetry (TG/DTA). The ion-exchange capacities (IECs), water uptake levels, and thicknesses of the AAEMs were measured. These AAEMs have potential for application in low temperature fuel cell systems.