A low-pressure high-recovery (LPHR) multistage reverse osmosis desalination process is developed in order to produce a very strong brine and freshwater at the same time. The specific energy consumption (SEC) of the process is estimated to be lower than that of a single-stage RO unit and comparable to previously proposed multistage RO configurations. An important feature of this process is that the operating pressure can be optimized to minimize the total cost of water production. The performances of the 4- and 5-stage configurations of the LPHR process are evaluated initially at the thermodynamic limit in terms of the specific energy consumption and total cost of producing water. The cost analysis suggest that the LPHR process would be economically feasible for a water recovery > 70% with an OPD between 58 and 65 bar in order to produce a freshwater product containing no more than 350 ppm TDS from a seawater feed with 35,000 ppm TDS. A process design is also proposed based on commercially available desalination membranes, predicting that 73% overall water recovery can be achieved at a maximum applied pressure of 55 bar using the 5-stage configuration of the LPHR process.