The first-principles thermodynamics characterization of the stabilities and electronic properties of the LaAlO3 (001) and (110) polar surfaces was systematically performed using density functional theory methods. Two types of polar surfaces, including the terminations along the (001) orientation (the LaO-and AlO2-terminated surfaces) and (110) orientation (the LaAlO-, O2-, La-, AlO-, and O-terminated surfaces),were considered in this study. The computational results of the charge redistributions and geometries confirm that the electronic structure change and surface reconstruction should be responsible for the cancellation of the macroscopic dipole moments of these polar terminations, which stabilizes them. The charge neutralization can also be achieved by the charge redistribution of surface atoms. Furthermore, using the surface grand potential method, in which the effect of the chemical environment on surface stability is considered, we constructed the stability phase diagram of the LaAlO3 (001) and (110) polar surfaces. The results indicate that only the O (110), LaO (001) and AlO2 (001) terminations have corresponding stability domains and can be considered targets in further experimental investigations.