In this paper we present the design of a Luneburg type of lens antenna, with a flat base, designed for wide angle scan. The antenna consists of a 11-layer lens, fed at its base by a 6×6 array of waveguides. The lens is broadband and has a very high aperture efficiency, only 1 dB below that of a reference aperture antenna with a uniform amplitude and phase. Its sidelobe level is good, only −21 dB at boresight and −13 dB for a scan angle of 64°. Its performance is shown to be considerably superior to that of a flat Luneburg lens previously reported in the literature, both in terms of the gain and scan capability, as well as the ease of fabrication.