The great potential of nanoporous membranes for water filtration and chemical separation has been challenged by the trade-off between selectivity and permeability. Here we report on nanoporous polymer membranes with an excellent balance between selectivity and permeability of ions. Our membranes are fabricated by irradiating 2-μm-thick polyethylene terephthalate Lumirror® films with GeV heavy ions followed by ultraviolet exposure. These membranes show a high transport rate of K+ ions of up to 14 mol h-1 m-2 and a selectivity of alkali metal ions over heavy metal ions of >500. Combining transport experiments and molecular dynamics simulations with a polymeric nanopore model, we demonstrate that the high permeability is attributable to the presence of nanopores with a radius of ~0.5 nm and a density of up to 5 × 1010 cm-2, and the selectivity is ascribed to the interaction between the partially dehydrated ions and the negatively charged nanopore wall.