GaN/AlGaN THz quantum-cascade laser (QCL) structures were grown on AlGaN/Si templates by a metal-organic chemical vapor deposition (MOCVD). We aim to fabricate a double metal waveguide (DMW) based GaN THz QCL through removing the Si substrate by wet etching. The DMW is essential for realizing low cavity loss and a very high optical confinement factor (99%). We grew 100 periods of GaN/Al0.21Ga0.79N two quantum wells (QW) type active region on Al0.08Ga0.92N/Si templates. Samples were evaluated by cross-sectional transmission-electron microscopy (TEM) and high-resolution X-ray diffraction (HR-XRD). We found that the full width at half maximum (FWHM) of the XRD satellite peaks became narrower when the growth temperature decreased, and the steepness of the QC layer hetero-interfaces has been improved.