This work studied the luminescent and electric properties of Cu-doped ZnO films grown on MgO (100) substrate by plasma-assisted molecular beam epitaxy. The doping quantity was controlled by regulating Cu Kundsen cell temperature. The crystallinity and surface morphology of the Cu-doped ZnO films were characterized by high resolution X-ray diffraction, atomic force microscopy, and scanning electron microscopy. The chemical state and elemental compositions was analyzed by X-ray photoelectron spectroscopy (XPS). The near-band-edge emission (NBE) and defect-related emission (DLE) were analyzed by photoluminescence spectroscopy. The electric properties were determined by Hall measurement and four-point probe measurement. The experimental results revealed that ZnO films grown epitaxially on MgO substrate with (10-10)ZnO//(100)MgO. X-ray rocking curve measurements showed that the (10-10)ZnO reflection exhibits a full width at half maximum value of about 0.7o-1.0o. The XPS analysis showed that the doped copper atoms have a monovalent state in the ZnO films grown at Cu Kundsen cell temperatures lower than 900oC. The amount of Cu incorporation was estimated to be in the range of 1x1019 to 1x1021 atoms/cm3. The NBE peak of the Cu-doped ZnO films can be deconvoluted into three sub-peaks: a free exciton emission at 3.29 eV, a basal-plane stacking fault emission at 3.19 eV, and a third peak at 3.25 eV. The third peak might be related to an acceptor-bound excitons due to the doping of copper, since it disappeared after annealing. Hall measurement indicated that both pure and Cu-doped ZnO films are n-type semiconductor. The electron concentration of undoped ZnO film is 1x1018 cm-3, whereas that of the Cu-doped ZnO films are in the range of 5x1015~5x1016 cm-3. Obviously, the electron concentration of ZnO is compensated by the substitution of Cu+ to Zn2+ which generates acceptor levels. However, the electron concentration of the Cu-doped ZnO films rose back to the order of magnitudes 1018 cm-3 after annealed in oxygen or hygrogen, indicating the acceptor states were eliminated. Moreover, in this study, the incorporation of copper in ZnO does not result in an increase of the yellow-green luminescence.