Over the past decades, desalination by reverse osmosis (RO) membranes has attracted increasing attention. Although RO has proven its efficiency, it remains, however, relatively costly because of the use of high-pressure pumps and the low water permeability of conventional cross-linked polymer membranes. One route to improve the desalination performance consists of using membranes made from sub-nanoporous boron nitride (sNBN) monolayers. Indeed, by using molecular dynamics simulations, we report here that the water permeability of such sNBN membranes far exceeds that of conventional RO polymer membranes and is even higher than that of nanoporous graphene while the ion rejection remains close to 100%. At the same time, the molecular mechanism of water and ion transport through sNBN has been elucidated, with special attention paid to the impact of ions on water permeability through sNBN membranes.