High quality ZnO films were grown on c-plane sapphire (c-Al O) substrates by plasma-assisted molecular beam epitaxy (P-MBE). The influence of Zn/O ratio on the epitaxial growth of ZnO is investigated. Via adjusting Zn/O ratio, structural, electrical and optical properties of the ZnO thin films are significantly improved, and the highest quality ZnO film with the full width of half maximum (FWHM) of 0.05° at the (0 0 2) peak and electron mobility of 54 cm/V s is obtained at the Zn/O ratio of 1.03. When the Zn/O ratio is diverged from 1.03, the films exhibit rough surface with reticulated nanostructures. The formation mechanism of the ZnO nanostructure at non-stoichiometric condition is discussed. It is also found that both Zn-rich and O-rich samples show DX emission peak located at 3.362 eV in the PL-spectra. By using the photon energy of the DX and the Haynes rules, the ionization energy of the donor corresponding to the DX is calculated to be 36 meV, which implies that the DX is related to hydrogen donor.