In this study, we present a simple ultraviolet (UV) light photodiode by transferring a layer of graphene film on single-crystal ZnO substrate. The as-fabricated heterojunction exhibited typical rectifying behavior, with a Schottky barrier height of 0.623 eV. Further optoelectronic characterization revealed that the graphene-ZnO Schottky junction photodiode displayed obvious sensitivity to 365-nm light illumination with good reproducibility. The responsivity and photoconductive gain were estimated to be 3×10⁴ A/W and 10⁵, respectively, which were much higher than other ZnO nanostructure-based devices. In addition, it was found that the on/off ratio of the present device can be considerably improved from 2.09 to 12.1, when the device was passivated by a layer of AlO_x film. These results suggest that the present simply structured graphene-ZnO UV photodiode may find potential application in future optoelectronic devices.