The surface morphology of epitaxially grown CeO2 layers on Si(100) and Si(111) substrates was studied using atomic force microscopy (AFM) and transmission electron microscopy. It was found that the CeO2(111)/Si(111) surface has a triangular-pyramidal hillock structure consisting of three (111) facets. In contrast, the CeO2 layer grown on Si(100) has (110) orientation and a periodically corrugated structure with gable roof shaped stripes consisting of two (111) facets. Quantitative analyses of AFM data reveal that as the layer thickness increases, the surface structure grows in size : the surface roughness increases monotonically for CeO2(111), whereas it saturates for CeO2(110).