This paper presents the design of a novel multi-beam Luneburg lens antenna with specific dielectric structure and proposes a new solution for downsizing planar lens antennas. The quasi-conformal transformation optics (QCTO) principle is applied to achieve an equivalent transformation relation between the spatial coordinate and the electromagnetic properties of material, effectively preserving the behavior of electromagnetic waves while achieving a significant reduction in antenna size. The antenna comprises a deformed Luneburg lens with a radius equivalent to