We measured the high-pressure x-ray diffraction of the giant dielectric constant material Ca Cu3 Ti4 O12 (CCTO) under both hydrostatic and uniaxial compressions. We found that the cubic structure of CCTO is stable up to 57 GPa. Nevertheless we observed that CCTO has unusual compression behaviors under hydrostatic pressure. Specifically, the volume reduction is less than that under uniaxial compression below 25 GPa, above it the volume reduction starts to approach and finally reaches the same value as that under the uniaxial compression at about 30 GPa. We explained these remarkable phenomena by using the model that the samples are composed of grains that have shells stiffer than the cores.