The energetics and diffusion of water molecules and hydrated ions (Na+, Cl-) passing through nanopores in graphene are addressed by dispersion-corrected density functional theory calculations and ab initio molecular dynamics (MD) simulations. Pores of about 0.8 nm in diameter with different pore-edge passivations, with (H) and (O, H) atoms, were considered. Our MD simulations show a water flux through the hydroxylated pores of about one H2O molecule every three picoseconds, in close agreement with recent experiments that estimated a water flux of three molecules per picosecond through pores of ∼1 nm. We also find that both pores are effective in blocking hydrated Na+ and Cl- ions with large energy barriers, ranging from 12 to 15 eV. In addition, pore passivation with O atoms would increase the water transport through hydroxylated pores, due to the formation of hydrogen bonds with nearby water molecules, which is not observed in the hydrogenated pores.