This paper describes the study on the electrical design of a multi-beam large antenna for a satellite payload. This satellite antenna provides the universal communication and broadcasting services to personal portable terminals over the Korean Peninsula. The structure of the hybrid antenna fed by a feed array is proper to provide multi-beams. The amplitude and phase of each feed element should be optimized for a required beam and they can be obtained by GO (Geometrical Optics) and PO(Physical Optics) method. The number of feed elements are also optimized to meet the specification of EIRP(Effective Isotropically Radiated Power). The optimally designed antenna with the limited reflector size and minimum number of feed elements is shown in this paper.