The main function of a Fresnel lens is to provide light guidance. Since the current LED sources cannot provide enough flux for reading lamps to be designed with a single LED, instead systems must use multiple LEDs. We present an optimal design of a Fresnel lens for a reading light system with multiple light sources of white light LEDs. The groove angles of the Fresnel lens are chosen as design parameters and the design goal is to maximize the illuminance in a specified reading surface while maintaining the distribution uniformity of the light rays. We develop a series of genetic algorithms that are implemented with SCHEME language and macros supported by the commercially available nonimaging optical simulation tool to search for a set of optimal groove angles for the Fresnel lens. From the simulation results we can see that the optimally designed Fresnel lens indeed offers better light-guiding performance than typical Fresnel lenses for a multiple-LED reading light system.