Al particles are widely used as a metal reductant in the thermite, and a native Al2O3 film always forms on the particle surface as a passivating oxide shell. The diffusions of Al and O atom through the oxide shell will influence the structure and thermodynamic properties of Al2O3, and thus the ignition process of the thermite. In this work, the thermodynamics properties of -Al2O3, -Al2O3 doped by Al interstitial atom and -Al2O3 doped by O interstitial atom under high pressure and temperature are comparatively investigated by the first-principles calculations based on density-functional theory and quasi-harhmonic Debye model. The effects of the doping of Al and O interstitial atoms on the thermodynamic properties of -Al2O3 are discussed. The results indicate that the doping of the Al and O interstitial atoms will reduce the bulk modulus, and increase the volume thermal expansion coefficient and constant volume heat capacity of -Al2O3. Therefore, the diffusions of Al and O atom will make the oxide shell more ductile, and adverse to the spallation during the ignition of Al particles.