In this work, we have study the low-temperature (77 K) and high-pressure Raman, photoluminescence (PL) spectroscopy and Heyd-Scuseria-Ernzerh (HSE) of hybrid functional theory calculation of wurtzite-type GaN based on our self-designed low-temperature and high-pressure experimental apparatus. The Raman spectroscopy indicates that the Raman vibration modes of GaN exhibit a blue shift at 77 K, but the blue shift gradually disappears at higher pressures. The PL spectroscopy shows that the zero-pressure band gap of GaN is 3.470 eV at the 77 K and it increases with increasing pressure. In addition, band gap values of GaN under high pressure have also been calculated by HSE hybrid functional theory. The pressure dependence of the calculated result is consistent with the experimental measurement. The energy of the exciton (ΓBX) increases with increasing pressure, and the relationship between the exciton energy (77 K) and pressure can be fitted to E(P)=3.470+2.89×10-2P+1.1×10-3P2 eV.