White nanosheets, yellow nanoislands and purple nanorods of CeO₂ have been synthesized by a hydrothermal method. Indirect and direct photon energies of CeO₂ of the white nanosheets (1.8, 2.1 eV), yellow nanoislands (2.2, 2.4 eV) and purple nanorods (2.0, 2.2 eV) are demonstrated, respectively. The difference in the electron spin–orbit coupling states between Ce 3d and O 2p may play an important role in their band gap energies.