Nano-sized powders of CaCu
3Ti
4O
12 were synthesized by a polymerized complex method and calcined at 600, 700 and 800 °C in air for 8 h. The diameter of the powders ranges from 30 to 100 nm. The CaCu
3Ti
4O
12 powders were characterized by TG-DTA, XRD, FTIR, SEM and TEM. Sintering of the powders was conducted in air at 1100 °C for 16 h. The XRD results indicated that all sintered samples have a typical perovskite CaCu
3Ti
4O
12 structure with some amount of CaTiO
3 and CuO. SEM micrographs of the sintered CaCu
3Ti
4O
12 ceramics showed the average grain size of 10–15 μm. The samples exhibit a giant dielectric constant,
′ of 10,000–20,000. It is found that
is independent on the frequency and weakly dependent on temperature. The Maxwell–Wagner polarization mechanism is used to explain the high permittivity in these ceramics. It is also found that all three sintered samples have the same activation energy of grains, which is 0.116 eV. On the other hand, the activation energy of grain boundaries is found to be 0.219, 0.391 and 0.641 eV for CaCu
3Ti
4O
12 ceramics prepared using the CaCu
3Ti
4O
12 powders calcined at 600, 700 and 800 °C, respectively.