The reverse osmosis (RO) desalination capability of hydrogenated and hydroxylated graphene nanomesh membranes (GNMs) inspired by the morphology of carbon nitride (C2N) has been studied by using molecular dynamics simulation. As an advantage, water permeance of the GNMs is found to be several orders of magnitude higher than that of the available RO filters and comparable with highly strained C2N (S-C2N) as follows: 6,6-H,OH > 12-H > S-C2N > 5,5-H,OH > 10-H. The reverse order is found for salt rejection, regardless of S-C2N. The hydrophilic character of the incorporated -OH functional group is believed to be responsible for linking the water molecules in feed and permeate sides via the formation of strong hydrogen bonds. This leads to a remarkable reduction in resistance of water molecules during penetration across GNMs. In fact, water permeance and salt rejection of the GNMs are controllable by adjusting the effective size and chemistry of their nanopores, while these kinds of adjustments are principally impossible for C2N, resulting in limiting the water permeance. More importantly, the C2N nanofilter works efficiently only under high tensile strain, which is not so straightforward in practice. These observations are also verified by computing electrostatic potential map interaction and barrier energies for transportation of water molecules/ions through GNMs based on quantum chemistry aspects.