Abstract: The Luneburg lens antenna is composed of a series of concentric shells of constant permittivity. Considering the complexity of numerical calculation, this paper presents a closed-form approach, which combines the spherical vector wave method and the reciprocity theorem. The hybrid method first calculates the scattered fields of the Luneburg lens using the spherical vector wave method. Then it transforms the calculated results into the radiation fields in the far region using the reciprocity theorem. This paper applies the approach to investigate the characteristics of the Luneburg lens in the focal region as well as in the far region. The effects of the shell number and the air gaps between the layers on the antenna performance have been also investigated. In the end, the paper presents the analysis result on the feasibility of the multiple-beam Luneburg lens antenna for satellite communication.