We report strong excitonic transitions and exciton-phonon couplings in the photoluminescence (PL) of ZnO thin films grown on MgO/sapphire (buffer/substrate) by plasma-assisted molecular-beam epitaxy. The room temperature (RT) PL spectra showed that the dominant emission contributions from the front surface area (FS) and the back surface area (BS) are the free exciton (FX) emission and its first longitudinal optical (LO)-phonon replica, respectively. We found that the one LO-phonon replica at the BS of ZnO can be even more intense than the direct (zero-phonon) FX transition at elevated temperatures. Time-resolved PL spectra revealed that the lifetime of FX recombination from FS is longer than that from BS, which is attributed to the reduction of nonradiative recombination at FS. This indicates that the existence of native defects or trap centers, which can be reduced by the proper initial growth condition, and the exciton-phonon interaction couplings play important roles in the excitonic transition properties of ZnO thin films.