By creating nanoscale pores in a layer of graphene, it could be used as an effective separation membrane due to its chemical and mechanical stability, its flexibility and, most importantly, its one-atom thickness. Theoretical studies have indicated that the performance of such membranes should be superior to state-of-the-art polymer-based filtration membranes, and experimental studies have recently begun to explore their potential. Here, we show that single-layer porous graphene can be used as a desalination membrane. Nanometre-sized pores are created in a graphene monolayer using an oxygen plasma etching process, which allows the size of the pores to be tuned. The resulting membranes exhibit a salt rejection rate of nearly 100% and rapid water transport. In particular, water fluxes of up to 10(6) g m(-2) s(-1) at 40 °C were measured using pressure difference as a driving force, while water fluxes measured using osmotic pressure as a driving force did not exceed 70 g m(-2) s(-1) atm(-1).