Nanoporous materials exhibit promising potential in water transportation applications, especially in ocean water desalination. It is highly desired to have great permeability, selectivity and controllability in the desalination performance of these nanopores. However, it is still a challenge to achieve all three features in one material or device. Here, we demonstrate efficient and controllable water desalination with a nanoporous 2D Fe phthalocyanine (FePc) membrane using molecular dynamics simulations. We find the FePc membrane not only conducts fast water flow, but it also suppresses ion permeation. The selectivity is attributed to a mechanism distinct from the traditional steric exclusion: cations are excluded due to electrostatic repulsion, whereas anions can be trapped in the nanopore and induce the reorganization of ions in the vicinity of the nanopore, which in turn creates a tendency for the trapped anions to move back into the saline reservoir. More interestingly, we find such mechanism is largely due to the sufficiently strong electrostatic interaction of the charged nanopore region with ions and is not restricted to the FePc nanopore. In addition, the number of protonated nitrogen atoms in FePc pores can be modulated by adjusting the pH value of the solution. The extent of the anion occupancy can thus be regulated, giving rise to control of the water flow. Taken together, great permeability, selectivity and controllability can be achieved with this nanosheet system. Moreover, our study suggests there is an alternative mechanism of water desalination which may be realized by intrinsically nanoporous materials such as FePc membranes.