Due to their high melting temperature and low thermal conductivity, zirconia (ZrO2) based ceramics have been widely used for thermal barrier coating materials. This study investigates zirconia's properties using the first principles calculations. Structural properties, including band structure, density of state, lattice parameter, as well as elastic constants for both monoclinic and tetragonal zirconia were computed. Pressure based phase transition of tetragonal zirconia (t-ZrO2) was also calculated, based on tetragonal distortion and band structure under compressive pressures. The results predicted a transition from monoclinic structure to a fluorite-type cubic structure at the pressure of 37 GPa. Moreover, monoclinic zirconia (m-ZrO2) thermodynamic property calculations were carried out. Temperature-dependent heat capacity, entropy, free energy, and the Debye temperature of monoclinic zirconia, from 0 to 1000 K, were computed and compared well with those reported in literature.