Current-driven magnetic domain wall motion is demonstrated in the quaternary ferromagnetic semiconductor ͑Ga,Mn͒͑As,P͒ at temperatures well below the ferromagnetic transition temperature, with critical currents of the order 10 5 A cm −2 . This is enabled by a much weaker domain wall pinning compared to ͑Ga,Mn͒As layers grown on a strain-relaxed buffer layer. The critical current is shown to be comparable with theoretical predictions. The wide temperature range over which domain wall motion can be achieved indicates that this is a promising system for developing an improved understanding of spin-transfer torque in systems with strong spin-orbit interaction.