Low-temperature epitaxy of MgxZn1-xO thin films is achieved on sapphire substrates by the reactive electron beam evaporation. X-ray diffraction (XRD) and energy dispersive x-ray (EDX) analyses of the films demonstrate that the structure of MgxZn1-xO depends upon the concentration of Mg in the films. With the increase of Mg concentration, the structure of MgxZn1-xO changes from the wurtzite crystal structure of ZnO to the cubic one with lattice constant similar to that of MgO. By the measurements of UV-visible transmission and ultraviolet photoluminescence spectra of the MgxZn1-xO films, it is found that the absorption band edge of MgxZn1-xO is blue shifted obviously with the increase of Mg concentration, indicating the absorption band edge of MgxZn1-xO becomes wider. However, the lattice mismatch between cubic MgxZn1-xO film and MgO is small (0.16%).