In this work, using milli-eV inelastic X-ray scattering, we showed that in a strongly disordered superlattice system, the phonon population shows a deviation from equilibrium. We developed a theoretical model which map the phonon transport into a 1D Bose-Hubbard model for optical lattices, with known many-body-localization. The work provides strong evidence on realizing the exotic many-body localization phenomena in a solid-state material.