The 5d-transition-metal pyrochlore oxide Cd2Re2O7, which was recently suggested to be a prototype of the spin-orbit-coupled metal [Phys. Rev. Lett. 115, 026401 (2015)10.1103/PhysRevLett.115.026401], exhibits an inversion-symmetry-breaking (ISB) transition at 200 K and a subsequent superconductivity below 1 K at ambient pressure. We study the crystal structure at high pressures up to 5 GPa by means of synchrotron x-ray powder diffraction. A rich structural phase diagram is obtained, which contains at least seven phases, and is almost consistent with the electronic phase diagram determined by previous resistivity measurements. Interestingly, the ISB transition vanishes at ∼4GPa where the enhancement of the upper critical field was observed in resistivity. Moreover, it is shown that the point groups at 8 K, probably kept in the superconducting phases, sequentially transform into piezoelectric, ferroelectric, and centrosymmetric structures on the application of pressure.