The thermodynamic and elastic properties of magnesium silicate (MgSiO3) perovskite at high pressure are investigated with the quasi-harmonic Debye model and the first-principles method based on the density functional theory. The obtained equation of state is consistent with the available experimental data. The heat capacity and the thermal expansion coefficient agree with the observed values and other calculations at high pressures and temperatures. The elastic constants are calculated using the finite strain method. A complete elastic tensor of MgSiO3 perovskite is determined in the wide pressure range. The geologically important quantities: Young's modulus, Poisson's ratio, Debye temperature, and crystal anisotropy, are derived from the calculated data.