Cadmium telluride (CdTe) has been studied using synchrotron powder X-ray diffraction in a diamond anvil cell up to 63 GPa at room temperature combined with density functional calculations. The experiment reveals two pressure-induced structural phase transitions with the following sequence: Rocksalt → Cmcm (12 GPa) → post-Cmcm (42 GPa). The crystal structure of the long-sought post-Cmcm phase is characterized. It has a monoclinic unit cell and the P21/m space group. Calculation confirms this phase transition sequence and further predicts a P21/m to P4/nmm transition near 68 GPa. Interestingly, the enthalpy of CdTe is found to be higher than the enthalpy sum of its constituents Cd and Te at pressures higher than 34 GPa. This suggests that CdTe becomes a high-enthalpy compound at high pressure. Extraordinary dynamic stability revealed in the phonon dispersion relations prevents the decomposition of CdTe at high pressure.