In this study, we tried to deposit ZnO films on Al₂O₃ (0001) and (112(-)0) substrates as buffer layers. ZnO and as-grown MgB₂ films were deposited using molecular beam epitaxy (MBE). The crystallinity and superconductivity of the MgB₂/ZnO film were studied using in-situ RHEED, XRD, resistance and a SQUID magnetometer. The ZnO layer was grown epitaxially on both of the substrates. From XRD θ-2θ scans, MgB₂ films were observed only at MgB₂-0001 and -0002 peaks and the T_c of these films was about 35 K. We discuss the effect of ZnO buffer layers for fabricating high-quality as-grown MgB₂ films.