Non-polar m-plane GaN terahertz quantum cascade laser (THz-QCL) structures have been studied. One is traditional three-well resonant-phonon (RP) design scheme. The other is two-well phonon scattering injection (PSI) design scheme. The peak gains of 41.8 and 44.2 cm−1 have been obtained at 8.2 and 7.7 THz respectively at 300 K according to the self-consistent non-equilibrium Green’s function calculation. Different from the usual GaAs two-well design, the upper and lower lasing levels are both ground states in the GaN quantum wells for the PSI scheme, mitigating the severe broadening effect for the excited states in GaN. To guide the fabrication of such devices, the doping effect on the peak gain has been analyzed. The two designs have demonstrated distinct doping density dependence and it is mainly attributed to the very different doping dependent broadening behaviors. The results reveal the possibility of GaN based THz-QCL lasing at room temperature.