A ZnO film with two-dimensional periodic structure was grown on Si substrate by radio-frequency plasma-assisted molecular beam epitaxy. The influence of wet-chemical etching on Si (100) and Si (111) substrates patterned with dot arrays was investigated for achieving a ZnO film with good periodic structure. X-ray diffraction and scanning electron microscopy mesurements demonstrate better crystalline quality and surface morphology of ZnO film grown on Si (111) than that on Si (100). The results suggest that the growth method is feasible for the fabrication of ZnO film with good periodic structure.