Energy relaxation dynamics in the Harper model coupled with a small number of phonon modes is numerically investigated. In the case of the Harper model irreversible energy transport between the electron and the phonon mode, which have been observed in the case of disordered systems, can be observed independent of the potential strength. In the irreversible energy flow, the role of the localization or randomness can be confirmed in comparison to the results in a periodic or disordered system. The coherent state representation of an autonomous phonon mode during the relaxation of the energy are also shown to confirm the process of phase randomization.