The inability of membranes to handle a wide spectrum of pollutants is an important unsolved problem for water treatment. Here we demonstrate water desalination via a membrane distillation process using a graphene membrane where water permeation is enabled by nanochannels of multilayer, mismatched, partially overlapping graphene grains. Graphene films derived from renewable oil exhibit significantly superior retention of water vapour flux and salt rejection rates, and a superior antifouling capability under a mixture of saline water containing contaminants such as oils and surfactants, compared to commercial distillation membranes. Moreover, real-world applicability of our membrane is demonstrated by processing sea water from Sydney Harbour over 72 h with macroscale membrane size of 4 cm2, processing ~0.5 L per day. Numerical simulations show that the channels between the mismatched grains serve as an effective water permeation route. Our research will pave the way for large-scale graphene-based antifouling membranes for diverse water treatment applications.