This letter presents a gap-waveguide phase shifter based on ridged unit cells with glide-symmetric configuration. The proposed unit cell design provides a higher stable phase shift compared to a conventional ridged  unit cell whose ridge height and waveguide width are tuned to achieve a stable phase shift. Through the insertion of glide-symmetric holes with semi-circle base in the ridged waveguide, a stable phase shift in a wide frequency range is achieved. Depending on the radii of the holes, the operating frequency range of the phase shifter can be tuned. A 90^o phase shifter in millimeter-wave range is designed and manufactured to validate the analysis. The experimental results reveal a 85^o +- 5^o phase shift from 33 GHz to 43 GHz (26.3% bandwidth). In this bandwidth, the reflection coefficient is below -10 dB with a maximum insertion loss of 0.7 dB.