Water security is a pressing issue for global citizens in the 21st century. Concerns over clean water supply, and the environmental impact of industrial waste water, make water treatment a world-wide problem requiring a simple and effective solution. Membrane distillation is an emerging water purification technique that complements state-of-the-art reverse osmosis processes. Membrane distillation achieves high rejection over a range of salt concentrations while maintaining flux, using a temperature differential as opposed to pressure across the membrane. Importantly the process can be driven using low grade waste heat energy. Current membranes used in membrane distillation do not guarantee stable membrane performance under harsh (high salt and acid or base concentrations) conditions. Here we report, a permeable graphene membrane operating in harsh conditions with no observable degradation. A permeate of pH neutral water with a flux of 25 ± 1 L m−2 h−1 is produced by this membrane through near (99.9 ± 0.1%) ion rejection from 0.6 M sodium chloride at pH 1 and pH 13, over 144 h. More complex ion solutions, including real acid mine drainage waste-water, were also successfully purified. These findings may present a membrane that is suitable to improve water supply and reduce the environmental impact of industrial waste-water.