Pure colossal dielectric constant oxide CaCu3Ti4O12 (CCTO) compound was prepared by traditional ceramic processing. Dielectric dispersion and complex impedances spectra were investigated using a impedance analyzer within a temperature range of 10—420 K. The data were simulated by “ZVIEW” software. The result indicates that there are two obvious relaxations in the dielectric dispersion spectra when the temperature is higher than room temperature and the dielectric constant increases remarkably with increasing temperatures at a low frequency, which indicates a thermal ionic polarization. However, the frequency spectra becomes similar to Debye-type relaxation when the temperature is lower than room temperature and the low-and high-frequency relaxation step almost keeps unchanged with temperature, which reveals a feature of interface polarization and considerable temperature stability for CCTO. The relaxation revealed in the frequency spectra corresponds to the three different semicircles revealed by the impedance spectra, which indicated there are three inhomogeneous regions or polarization processes in CCTO ceramics and the colossal dielectric constant mainly comes from the extrinsic polarization of these inhomogenities. The activation energies are found to be respectively 0.05 eV, 0.58 eV and 0.49eV for the three different polarization processes by simulating the impedance semicircles using an equivalent circuit.