Permeation through membrane with pores is important in the choice of materials for filtration and separation techniques. Here, we report by the molecular dynamics simulations that a single-layer graphyne membrane can be impermeable to salt ions, while it allows the permeation of water molecules. The salt rejection and water permeability of graphyne are closely related to the hydrostatic pressure, type of graphyne membrane, and the salt concentration of solution, respectively. By analyzing hydration shell structure, we found that the average coordination number of ions plays a key role in water purification. Our calculation showed that the salt rejection of the graphyne-3 membrane is the best and it can keep an ideal rate of 100% in consideration cases. In comprehensive evaluation of both salt rejection and permeability, the graphyne-4 is a perfect purification membrane. To sum up, our results indicated that the graphynes (graphyne-3 and -4) not only have higher salt rejection but also possess higher water permeability which is several orders of magnitude higher than conventional reverse osmosis membranes. The single-layer graphyne membrane may have a great potential application as a membrane for water purification.