We propose and study the feasibility of a THz GaN/AlGaN quantum cascade laser (QCL) consisting of only five periods with confinement provided by a spoof surface plasmon (SSP) waveguide for room temperature operation. The QCL design takes advantages of the large optical phonon energy and the ultrafast phonon scattering in GaN that allow for engineering favorable laser state lifetimes. Our analysis has shown that the waveguide loss is sufficiently low for the QCL to reach its threshold at the injection current density around 6 kA/cm2 at room temperature.