High-quality CeO2 films were grown on Al2O3(0001) substrates using oxygen plasma-assisted molecular beam epitaxy. The epitaxial orientation of the films is found to be CeO2(100) and CeO2(111) at low (≪8 Å/min) and higher growth rates (≫12 Å/min), respectively. CeO2(100) film grows as three-dimensional islands, while CeO2(111) film grows as two-dimensional layers. The CeO2(100) film exhibits better epitaxial quality compared to CeO2(111) film. However, the CeO2(100) film on Al2O3(0001) shows three in-plane domains at 30° to each other. While the epitaxial quality is attributed to the close match between oxygen sublattices of CeO2(100) and Al2O3(0001), the three in-plane domains in CeO2(100) are attributed to the threefold symmetry of the substrate. The relative stability of different epitaxial orientations of CeO2 films on Al2O3(0001) obtained from molecular dynamics simulations strongly supports the experimental observations.