Osmotic power, also known as ‘blue energy’, is produced by mixing solutions of different salt concentrations, and represents a vast, sustainable and clean energy source. The efficiency of harvesting osmotic power is primarily determined by the transmembrane performance, which is in turn dependent on ion conductivity and selectivity towards positive or negative ions. Atomically or molecularly thin membranes with a uniform pore environment and high pore density are expected to possess an outstanding ion permeability and selectivity, but remain unexplored. Here we demonstrate that covalent organic framework monolayer membranes that feature a well-ordered pore arrangement can achieve an extremely low membrane resistivity and ultrahigh ion conductivity. When used as osmotic power generators, these membranes produce an unprecedented output power density over 200 W m−2 on mixing the artificial seawater and river water. This work opens up the application of porous monolayer membranes with an atomically precise structure in osmotic power generation.