The GaN/AlGaN multilayer structure for the active regions of terahertz quantum cascade lasers (QCLs) was grown by metal organic chemical vapor deposition (MOCVD). The surface morphology of the grown sample showed good surface quality with an average roughness of less than 1 nm. The x-ray diffraction pattern and transmission electron microscopy images showed that the well-controlled quantum cascade GaN/AlGaN layers were grown. The Fourier transform infrared spectrometer measurement showed a distinct A1 (LO) phonon frequency at 822 cm-1 that is red-shifted with respect to the single Al0.2Ga0.8N layer due to the good periodicity of the grown quantum cascade GaN/Al0.2Ga0.8N structure. MOCVD growth should be a viable technique for fabrication of AlGaN/GaN quantum cascade laser and phonon frequency shift should be a key indicator for the good periodicity of the grown QCL structure.