The thesis describes development of membranes containing nanopores with charged pore walls, which could be used for desalination of brackish water. Semipermeable membranes composed of high density conical nanopores have been proposed for desalination by reverse osmosis. These nanopores feature a bipolar surface charge pattern so that the pore walls contain a junction between a zone with positive surface charges and a zone with negative surface charges. In this work we seek to show that polyimide (PI) membranes containing conical nanopores with such surface charge pattern may be produced by the process of track-etching of commercially available Kapton 50HN foils. The membranes prepared had a nanopore density of ~108 per cm^2. Salt rejection of the membranes was probed using 100 mM KCl as the feed solution and pressure differences up to several atmospheres. Maximum rejection of ~55% was achieved in a single-step desalination process. Modeling of salt rejection was also performed using the coupled Poisson-Nernst- Planck and Navier-Stokes equations. Our results demonstrated that conically shaped nanopores with bipolar surface charge pattern could be used for desalination of brackish water.