We have recently developed a novel semiconductor, (ZnO)x(InN)1-x (abbreviated to ZION). In this study, we have succeeded in direct epitaxial growth of ZION films on 19–21%-lattice-mismatched c-plane sapphire by radio-frequency (RF) magnetron sputtering. X-ray diffraction analysis showed that there is no epitaxial relationship between ZION films fabricated at room-temperature (RT) and the sapphire substrates, while the films fabricated at 450oC grow epitaxially on the sapphire substrates. From the analysis of time evolution of the surface morphology, the process for the epitaxial growth of ZION on sapphire is found to consist of three stages. They are (i) initial nucleation of ZION crystallites with crystal axis aligned to the sapphire substrate, (ii) island growth from the initially formed nuclei and subsequent nucleation (secondary nucleation) of ZION crystallites, and (iii) lateral growth of ZION islands originated from initially formed nuclei. On the other hand, non-epitaxial ZION films fabricated at RT just grow in 3D mode. From these results, we conclude that the substrate temperature is the key to control of nucleation and subsequent epitaxial growth of ZION films on the lattice-mismatched substrate.