Desalination of sea saline water seems a successful solution to supply clean water. For desalination, novel nanoporous membranes have been proposed as a substitute for the classic reverse osmosis (RO) membranes. The one-atom-thick graphyne membrane has shown great potential in water desalination. By applying functional groups (FGs) into the pores of the monolayer graphyne membranes, the water permeability and the ion rejection were passively increased. The effects of applying various FGs such as Hydrogen, Fluorine, Carboxyl and Amine, effect of the salt concentration, the applied pressure, and the effective diameter of the graphyne pores were determined by molecular dynamics (MD) simulations. Also, the distribution of water density and hydrated ions structure were discussed. The results revealed that graphyne-4 with F FGs may be the best membrane for desalination. Compared with bare graphyne, this membrane increased the water permeability and the ion rejection for the various applied pressures of salt concentrations.