We investigate lattice thermal conductivity κ of MgSiO3 perovskite (pv) by ab initio lattice dynamics calculations combined with exact solution of linearized phonon Boltzmann equation. At room temperature, κ of pristine MgSiO3 pv is found to be 10.7 W/(m · K) at 0 GPa. It increases linearly with pressure and reaches 59.2 W/(m · K) at 100 GPa. These values are close to multi-anvil press measurements whereas about twice as large as those from diamond anvil cell experiments. The increase of k with pressure is attributed to the squeeze of weighted phase-spaces phonons get emitted or absorbed. Moreover, we find κ exhibits noticeable anisotropy, with κzz being the largest component and (max − min)/ being about 25%. Such extent of anisotropy is comparable to those of upper mantle minerals such as olivine and enstatite. By analyzing phonon mean free paths and lifetimes, we further show that the weak temperature dependence of κ observed in experiments should not be caused by phonons reaching ‘minimum’ mean free paths. These results clarify the microscopic mechanism of thermal transport in MgSiO3 pv, and provide reference data for understanding heat conduction in the Earth’s deep interior.