ZnO/Mg0.2Zn0.8O superlattices with a band-gap offset of about 0.5 eV were epitaxially grown by laser molecular-beam epitaxy on a sapphire(0001) substrate using a ZnO buffer layer. The superlattice structure with a period ranging from 8 to 18 nm was clearly verified by cross-sectional transmission electron microscopy, Auger depth profile, and x-ray diffraction. As the well layer thickness decreased below 5 nm, the photoluminescence peak and absorption edge in the photoluminescence excitation spectra showed a blueshift, indicating a quantum-size effect.