Total energy calculations of germanium nitride, done at three different phases under extreme conditions in the β, wII and γ structures using the plane-wave pseudo-potential method plus GGA-PBE in the framework of quantum mechanical density functional theory. Bulk properties such as the equilibrium lattice parameters, elastic constants and bulk moduli are predicted and compared to available theoretical and experimental data. γ-Ge3N4 could not resistant to thermal shocks due to its brittleness. The ductility of β-Ge3N4 is larger than that of wII-Ge3N4. The β → wII → γ phase transitions are also successfully predicted. The phase boundary of β → wII transition can be described as P = 10.80087 − 8.58508 × 10−4T + 5.00991 × 10−6 T2 − 1.84732 × 10−9 T3. Pressure (0–58 GPa) and temperature (0–1300 K) dependent thermal quantities including the bulk modulus, coefficient of thermal expansion, entropy, heat capacity and Debye temperature are obtained and analyzed through the quasi-harmonic approximation, in which the lattice vibrations and phonon effects are taken into account. Some interesting features can be observed in the temperature range of 300 ∼ 1200 K. It is worthy of note that most of the investigated properties are not reported by previous literatures. Our calculations need to be verified by the future experiments.