A beamforming antenna based on a spherical Luneburg lens operating at $3-4 \mathrm{GHz}$ is proposed. The antenna consists of a spherical lens with a radius of $0.8 \%_{0}$ (free-space wavelength of the central operating frequency) and five double-ridged waveguides. An approximation to an ideal Luneburg lens is realized by controlling the air-filling rate of a series of hollow dielectric cones with common vertices. By adopting the double ridge waveguide as the feed source, the requirement of the fan beam for the smaller aperture feed source is realized. The simulation results show that the aperture efficiency of the designed lens can reach $60 \%$, the synthetic beam is a fan beam with a width of 145°, and the gain flatness is better than $0.5 \mathrm{~dB}$ within ± 60°. The antenna has the advantages of small lens size, high aperture efficiency, and wide synthetic beam, and can be used for the deployment of 5G communication base stations.