Providing fresh and drinkable water is a grand challenge the world is facing today. Development in nanomaterials can create possibilities of using energy-efficient nanoporous materials for water desalination. In this work, we demonstrated that ultrathin conductive metal-organic framework (MOF) is capable of efficiently rejecting ions while giving access to high water flux. Through molecular dynamic simulation, we discovered perfect ion rejection rate by two-dimensional (2D) multilayer MOF. The naturally porous structure of 2D MOF enables significantly 3-6 orders of magnitude higher water permeation compared to that of traditional membranes. Few layers MOF membranes show 1 order of magnitude higher water flux compared to that of single-layer nanoporous graphene or molybdenum disulfide (MoS2) without the requirement of drilling pores. The excellent performance of 2D MOF membranes is supported by water permeation calculations, water density/velocity profiles at the pore, and the water interfacial diffusion near the pore. Water desalination performance of MOF offers a potential solution for energy-efficient water desalination.