We observed highly single crystalline epitaxial growth of CeO2 films on a (1 (1) under bar 0 2) (r-cut) Al2O3 (sapphire) using X-ray reflectivity and diffraction. The X-ray reflectivity data indicate a presence of a thin interfacial layer between CeO2 film and r-cut sapphire with a lower electron density than that of CeO2. Above the interfacial layer, the mechanism of film growth deduced from the reflectivity and diffraction data indicates two-dimensional layer growth. The surface roughness of 394 Angstrom thick Nm is 5 Angstrom, and the film shows nearly strain-free growth.