This paper presents the implementation of Luneburg lens antenna based on a 2-D parallel-plate structure for broadband multibeam radiation at millimeter-wave frequencies. In particular, each beam pattern of this 2-D Luneburg lens antenna has a narrow beamwidth along the multibeam dimension, and exhibits a broad beamwidth along the other cross section, analogous to the radiation from a 1-D array of antennas embedded inside the parallel-plate structure. Furthermore, the isolation to external structures by the top and bottom metal parallel plates may reduce the beam distortion from external interferences, and therefore enhance its compatibility to integrate with other radio frequency (RF) components to form an RF subsystem module. In addition, a theoretic model to realize the dielectric variation of Luneburg lens is developed by using stacked multiple planar layered dielectric materials for a cheap manufacture. In this paper, numerical simulation to validate the developed model of 2-D Luneburg lens design is first presented. Afterward, simulation and experimental measurement results of a practical design are both presented to validate the design concept.