A novel global optimization algorithm to solve nonconvex problem is used to find the global optimal design of reverse osmosis networks for seawater desalination. The objective is to determine the optimal process design and operating conditions for a given water production. The networks were designed by using hollow fiber reverse osmosis modules. The Kimura-Sourirajan model was used for describing transport phenomena of solute and water transport through the membrane. The concentration polarization phenomenon has been taken into account. It was mathematically described using the film theory. The objective function to be minimized is the cost, which includes capital investment (membrane cost, pumping and energy recovery system, intake and pretreatment systems, etc.) and operation and maintenance costs (membrane replacement, chemical treatment, spares, required and recovered energy, etc.). The proposed algorithm is deterministic and attains finite convergence to the global optimum. It is iterative and a main problem is solved each iteration. The main problem has convex constraints and a nonconvex objective function. The main problem solution indicates either a better solution for the original problem, or a region which can be discarded. Therefore, the feasible region to improve the objective function is reduced each iteration. The algorithm finishes when the whole region has been analysed and discarded. A bound reduction technique is performed in order to accelerate the convergence speed. The algorithm shows a good performance and efficient execution time. Different cases are solved in order to show the methodology and computational performance.