We demonstrate molybdenum disulfide (MoS2) as a nano porous membrane for water desalination. By performing extensive molecular dynamics simulations, we find that a nanopore in a single-layer MoS2 can effectively reject salt ions and allow transport of water at a high rate. More than 88% of ions are rejected by membranes having pore areas ranging from 20 to 60 A^2. Water flux through the nanoporous MoS2 membrane is found to be 2 to 5 orders of magnitude greater than that of other known nanoporous membranes (MFI-type zeolite, commercial polymeric seawater Reverse Osmosis (RO), brackish RO, Nanofiltration and High-flux RO). Pore chemistry and architecture are shown to play a significant role in modulating the water flux. MoS2 pores with only molybdenum atoms on their edges give rise to higher fluxes which are about 70% greater than that of graphene nanopores. These observations are explained by the permeation coefficients, energy barriers, water density and velocity distributions in the pores. Our findings pave way towards identifying efficient membranes for water desalination