In situ high pressure XRD diffraction and Raman spectroscopy have been performed on 12 nm CeO2 nanoparticles. Surprisingly, under quasihydrostatic conditions, 12 nm CeO2 nanoparticles maintain the fluorite-type structure in the whole pressure range (0-51 GPa) during the experiments, much more stable than the bulk counterpart (P-T similar to 31 GPa). In contrast, they experienced phase transition at pressure as low as 26 GPa under non-hydrostatic conditions (adopting CsCl as pressure medium). Additionally, 32-36 nm CeO2 nanoparticles exhibit an onset pressure of phase transition at 35 GPa under quasihydrostatic conditions, and this onset pressure is much lower than our result. Further analysis shows both the experimental condition (i.e., quasihydrostatic or non-hydrostatic) and grain size effect have a significant impact on the high pressure behaviors of CeO2 nanomaterials.