The structure, thermodynamic and elastic properties of magnesium silicate (MgSiO3) post-perovskite at high pressure are investigated with quasi-harmonic Debye model and ab initio method based on the density functional theory (DFT). The calculated structural parameters of MgSiO3 post-perovskite are consistent with the available experimental results and the recent theoretical results. The Debye temperature, heat capacity and thermal expansion coefficient at high pressures and temperatures are predicted using the quasi-harmonic Debye model. The elastic constants are calculated using stress–strain relations. A complete elastic tensor of MgSiO3 post-perovskite is determined in the wide pressure range. The calculated elastic anisotropic factors and directional bulk modulus show that MgSiO3 post-perovskite possesses high elastic anisotropy.