Desalination that produces clean freshwater from seawater holds the promise to solve the global water shortage for drinking, agriculture and industry. However, conventional desalination technologies such as reverse osmosis and thermal distillation involve large amounts of energy consumption, and the semipermeable membranes widely used in reverse osmosis face the challenge to provide a high throughput at high salt rejection. Here we find by comprehensive molecular dynamics simulations and first principles modeling that, pristine graphyne, one of the graphene like one­atom­thick carbon allotropes, can achieve 100% rejection of nearly all ions in seawater including Na+, Cl­, Mg2+, K+ and Ca2+, at an exceptionally high water permeability about two orders of magnitude higher than those for commercial state­of­the­art reverse osmosis membranes at a salt rejection of ~98.5%. This complete ion rejection by graphyne, independent of the salt concentration and the operating pressure, is revealed to be originated from the significantly higher energy barriers for ions than that for water. This intrinsic specialty of graphyne should provide a new possibility for the efforts to alleviate the global shortage of freshwater and other environmental problems.