Dielectric properties of pure phase BaTi0.99(Nb0.5Ga0.5)(0.02)O-3 ceramics, prepared via a conventional solid-state method, have been studied in the frequency range 0.01 Hz-10 MHz, at temperatures 130 degrees C to 200 degrees C. Colossal dielectric constant, epsilon(r)similar to 2 x 10(5), and low dielectric loss, tan delta similar to 0.05 at 1 kHz have been obtained. The permittivity showed weak frequency dependency in a broad range of frequency from 1 Hz to 30 kHz and less than +/- 20% capacitance deviation over the temperature range from 243 to 358 K. The AC impedance spectroscopy analysis indicated three relaxation mechanisms, the electrode interfacial polarization, internal bather layer capacitor effect and hopping polaron polarization contributed to the colossal dielectric constant.