Two-dimensional nanoporous membranes hold great promise for the design of state-of-the-art desalination architectures to alleviate the increasing global water scarcity. Herein, by employing molecular dynamics simulations, we demonstrate the great potential of two recently reported metal-organic frameworks (MOF) membranes, namely NiIT and NiAT, as efficient desalination membranes that reach super high water flux and high salt rejection. The desalination performance of the MOF membrane is highly tunable through controlling the membrane thickness from one layer to five layers. Double layer NiIT membrane exhibits excellent salt rejection of 100% for NaCl, and meanwhile achieving high water permeability of ∼45 L/cm2/MPa/day. While for the convertible double-layer NiAT, it effectively rejects ∼96% ions with an improved water permeation of over 70 L/cm2/MPa/day. Quantitative analysis of water distribution reveals a denser water solvation shell around NiAT membrane than NiIT and a higher water velocity through the nanopore of NiAT than that of NiIT, contributing to the enhanced water permeability. Through calculating free energy for water/ions translocating through two membranes, a clear energy barrier is observed for ions to penetrate through the sub-nanosized pores in both membranes, leading to the high salt rejection. The present study suggests that these two MOF membranes can serve as a promising semipermeable membrane for energy-efficient desalination which is highly prospective in industrial applications.