The x-ray diffraction study of 12 nm CeO2 was carried out up to similar to 40 GPa using an angle dispersive synchrotron-radiation in a diamond-anvil cell with different pressure transmitting medium (PTM) (4 : 1 methanol: ethanol mixture, silicone oil and none) at room temperature. While the cubic fluorite-type structure CeO2 was retained to the highest pressure, there is progressive broadening and intensity reduction of the reflections with increasing pressure. At pressures above 12 GPa, an unusual change in the compression curve was detected in all experiments. Significantly, apparent negative volume compressibility was observed at P = 18-27 GPa with silicone oil as PTM, however it was not detected in other circumstances. The expansion of the unit cell volume of cubic CeO2 was about 1% at pressures of 15-27 GPa. To explain this abnormal phenomenon, a dual structure model (hard amorphous shell and relatively soft crystalline core) has been proposed.