Nanoporous graphene and related atomically thin layered materials are promising candidates in reverse electrodialysis research owing to their remarkable ionic conductivity and high permselectivity. The synthesis of atomically thin nanoporous membranes with a narrow pore size distribution, however, remains challenging. Here, we report the fabrication of nanoporous carbon membranes via the thermal crosslinking of core-rim structured monomers, that is, polycyclic aromatic hydrocarbons. The mechanically robust, centimetre-sized membrane has a pore size of 3.6 ± 1.8 nm and a thickness of 2.0 ± 0.5 nm. When applied to reverse electrodialysis, the nanoporous carbon membrane offers a high short-circuit current with an output power density of 67 W m-2, which is about two orders of magnitude beyond that of the classic ion-exchange membranes and current prototype nanoporous membranes reported in the literature. Crosslinked and atomically thin porous polycyclic aromatic hydrocarbon membranes therefore represent new scaffolds that will revolutionize the rapidly developing fields of sustainable energy and membrane technology.