In this letter, we propose and study a 2-D glide-symmetric dielectric periodic structure. We demonstrate that glide symmetry broadens the bandwidth of operation and achieves lower effective refractive indices when compared to non-glide configurations. These two properties are beneficial for producing graded-index lens antennas. To demonstrate the potential of the proposed unit cell, we designed a Luneburg lens operating in the K- A nd Ka-bands. The lens was manufactured with conventional additive manufacturing and it has a potential use for future wireless communications given its low-cost and low-profile.