Nanocrystalline CaCu3Ti4O12 powders with particle sizes of 39.28 8.12 nm were synthesized by a simple modify sol-gel using PVP (Poly-vinyl-pyrrolidone). The synthesized precursor was characterized by TG-DTA to determine the thermal decomposition and crystallization temperature which was found to be at above 500 degrees C. The precursor was calcined at 800 degrees C in air for 8 h to obtain nanocrystalline powders of CaCu3Ti4O12. The calcined CaCu3Ti4O12 powders were characterized by XRD, FTIR, SEM and TEM. Sintering of the powders was conducted in air at 1100 degrees C for 16 h. The XRD results indicated that all sintered samples have a typical perovskite CaCu3Ti4O12 structure and a small amount of CaTiO3. SEM micrographs showed the average grain sizes of 1.86 +/- 0.69 /m for the sintered CaCu3Ti4O12 ceramic prepared using the CaCu3Ti4O12 powders calcined at 800 degrees C. The sintered samples exhibit a giant dielectric constant, epsilon' of approximately 10(3)-10(4). The large low-frequency dielectric permittivity at low temperature is closely related to sub-grain boundary distribution, including conductivity effect. Furthermore, the ceramic shows three semicircles in the complex impedance plane. However, at low frequency, semicircles of sub-grain boundary and grain boundary are considered to represent collapse different electrical mechanisms. The another is ascribed to the contribution of grain. The dielectric behavior at several frequencies and temperatures of these samples can be attributed to electronic inhomogeneities present in material and can be explained based on a microstructural model.