In this work, we design a planar half-Luneburg lens antenna. The gradient of refractive index is realized using a dielectric slab periodically loaded with air-cavities of varying size. The cavities are glide-symmetrically arranged. It is demonstrated that by introducing glide symmetry, the bandwidth and range of realizable refractive indices are increased compared to a non-glide-symmetric structure. The lens antenna operates from 22 to 32 GHz and can scan its directive beam over a 50 degree range in the H-plane. The side lobe level in this scan range is lower than -10 dB throughout the band.