Using density functional simulations, within the generalized gradient approximation and projector-augmented wave method, we study structures and energetics of CaSiO3 perovskite in the pressure range of the Earth's lower mantle (0-150 GPa). At zero Kelvin temperature the cubic (Pm (3) over barm) CaSiO3 perovskite structure is unstable in the whole pressure range, at low pressures the orthorhombic (Pnam) structure is preferred. At 14.2 GPa there is a phase transition to the tetragonal (I4/mcm) phase. The CaIrO3-type structure is not stable for CaSiO3. Our results also rule out the possibility of decomposition into oxides.