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A large class of metal superhydrides was found to be a conventional BCS superconductor under high pressures. In this work, we focused on cerium decahydride, CeH _10 . Ce is a member of the so–called lability belt in the periodic table, where the physical properties can be largely affected by pressure. It was reported and we confirmed that CeH _10 can be formed with the Fm-3m structure, where a cerium atom is embedded in a H _32 clathrate cage. Our phonon calculations show that it is dynamically stable at around 300 GPa onwards. We examined the evolution under pressures of the phonons, the electronic states, the Fermi surface, and the electron localization function (ELF). There exists a small van Hove singularity (vHs), and it gradually moves to below the Fermi surface as pressure increases. This behaviour associating with the reducing value of the electron-phonon coupling strength ( λ ), causes the superconductivity transition temperature (T _c ) to gradually reduce under pressures. The maximum T _c is 45 K at 300 GPa.