ZnO single crystal thin films were grown by plasma enhanced molecular beam epitaxy on (0 0 0 1) sapphire. The growth modes of ZnO epilayers were investigated by reflection high-energy electron diffraction. A transition from two-dimensional nucleation to three-dimensional nucleation is found at the initial growth stage. Optical properties of the films, studied by photoluminescence spectroscopy, exhibit a dominant bound exciton emission at 3.361 eV at 4 K, and a deep level emission centered at 2.42 eV which is associated with either impurities or native defects. The deep level emission which is successfully suppressed to 1500 of intensity of the excitonic emission. Fabrication of these high-quality ZnO epilayers had lead to observation of stimulated emission at room temperature.