The present invention discloses mixed matrix membranes (MMMs) comprising ion-exchanged molecular sieves such as UZM-5 zeolite ion-exchanged with Li.sup.+ cation (Li-UZM-5) and a continuous polymer matrix and methods for making and using these membranes. These MMMs, comprising ion-exchanged molecular sieves, in the form of symmetric dense films, asymmetric flat sheets, asymmetric hollow fibers, or thin-film composites, have exhibited simultaneously increased selectivity and permeability (or permeance) over polymer-only membranes and the mixed matrix membranes made from molecular sieves that have not been ion exchanged for gas separations. These MMMs are suitable for a variety of liquid, gas, and vapor separations such as desalination of water by reverse osmosis, deep desulfurization of gasoline and diesel fuels, ethanol/water separations, pervaporation dehydration of aqueous/organic mixtures, CO.sub.2/CH.sub.4, CO.sub.2/N.sub.2, H.sub.2/CH.sub.4, O.sub.2/N.sub.2, olefin/paraffin, iso/normal paraffins separations, and other light gas mixture separations.