All-vanadium redox flow batteries (VRBs) have attracted considerable interest as promising energy-storage devices that can allow the efficient utilization of renewable energy sources. The membrane, which separates the porous electrodes in a redox flow cell, is one of the key components in VRBs. High rates of crossover of vanadium ions and water through the membrane impair the efficiency and capacity of a VRB. Thus, membranes with low permeation rate of vanadium species and water are required, also characterized by low resistance and stability in the VRB environment. Here, we present a new design concept for amphoteric ion-exchange membranes, based on radiation-induced grafting of vinylpyridine into an ethylene tetrafluoroethylene base film and a two-step functionalization to introduce cationic and anionic exchange sites, respectively. During long-term cycling, redox flow cells containing these membranes showed higher efficiency, less pronounced electrolyte imbalance, and significantly reduced capacity decay compared to the cells with the benchmark material Nafion 117.