Based on the density functional theory (DFT) and using the plane waves ultra-soft pseudo-potential technique, some basic properties of Nb3AlN were simulated, such as ground electronic states and thermodynamic performances. The simulation results show that the properties of Nb3AlN were similar to those of metals, with good electrical conductivity and thermal conductivity. The heat capacity increases with increasing of temperature and decreasing of pressure. The Grüneisen parameter γ increases with increasing of temperature, and decreases non-linearly as the pressure climbs up. The Debye temperature is influenced by temperature and pressure, which decreases sharply with increasing of temperature and climbs up with the increasing of pressure rapidly. The simulation results of the relationship between Gibbs free energy and temperature show that Nb3AlN can be synthesized through an appropriate process.