The structural properties of MgSiO3-ilmenite at high pressures are determined using Ab initio variable cell-shape molecular dynamics. Our athermal results at zero pressure are in excellent agreement with single-crystal measurements. The predicted lattice constants compare favorably with powder X-ray diffraction data. The internal parameters are shown to vary only slightly with pressure. The c axis is considerably more compressible than the a axis and our results suggest that this anisotropic behavior arises in the relatively larger compressibility of MgO6 with respect to SiO6 octahedra. Both octahedral types remain highly distorted with the degree of distortion decreasing (more rapidly in MgO6) under compression. By comparing free energies, it is shown that MgSiO3 should transform from the ilmenite to the perovskite structure at 30 GPa (for static lattice). At the transition, the density and elastic moduli increase substantially.