In this study, via molecular dynamic simulations, we showed that the latest described graphene-like carbon nitride membranes, such as g-C4N3, g-C6N6, and g-C3N4 single-layers, can be used as high-performance membranes for water desalination. In addition to having inherent nanopores and extraordinary mechanical properties, the carbon nitride membranes have high water permeability and strong ion rejection (IR) capability. The important point about carbon nitride membranes is that the open or closed state of the pores can be changed by applying tensile stress and creating a positive strain on the membrane. The effect of the imposed pressure, the tensile strain, the ion concentration, and the effective pore size of the membranes are reported. It is demonstrated that, with the applied tensile strain of 12%, the g-C6N6 membrane is the best purification membrane, with a water permeability of 54.16 l cm−2 d−1 MPa−1 and the IR of 100%. Its water permeability is one order of magnitude greater than other one-atom-thick membranes.