In this Letter, we explore the dispersion of spoof surface plasmons supported by a single-layer glide-symmetric structure. This structure consists of an infinitely long double-notched slot perforated in a metal layer. The presence of a degeneracy of the two lowest-order modes at the Brillouin zone boundary, which have non-zero group velocity is explained and experimentally demonstrated. Further, the dependence of the band structure when glide-symmetric configuration is broken is also explored.