Reverse osmosis constitutes a large portion of currently operating commercial water desalination systems. Employing membranes with large water fluxes while maintaining high salt rejection is of central importance in decreasing the associated energy consumption and costs. The ultrathin-film nature of zeolite nanosheets and their versatile pore structures provides great opportunities in desalination. To push forward the development of zeolite nanosheets for water desalination, nonequilibrium molecular dynamics simulations were carried out to systematically study zeolites as RO membranes and establish fundamental structure-performance relationships. We have identified that zeolite nanosheets can achieve a high salt rejection rate close to 100% while allowing nearly 2 orders of magnitude higher water permeability than currently available membranes. Moreover, the effects of the pore density, inclusion of cages, and free energy barrier on water permeability and salt rejection are unraveled, leading to important insights toward the rational design of novel zeolite membranes.