SnO2-Zn2SnO4 composite ceramics with a colossal dielectric permittivity and varistor behavior are prepared by traditional ceramic processing. By increasing bias voltage from 0 to 10V at a low frequency (10(3)Hz) and at room temperature, the relative permittivity decreased rapidly from about 20000 to several thousand, whereas the radius of the semicircle in the complex impedance decreased and the tail gradually disappeared. However, the peak height and the position of the imaginary part of the complex modulus in the spectra were independent of the applied DC voltage. The slope deduced from the bias voltage-dependent straight lines of the double-logarithmic imaginary permittivity spectra were constant with a value of -0.63 at high frequencies and they decreased to -1 at low frequencies. The results strongly indicate that a number of weekly trapped charges existed in the ceramic bulk. From the temperature-dependent dielectric and electric modulus spectra, the trapped charge activation energy was about 0.32eV, which may be associated with the oxygen vacancies. Based on the results, a modified equivalent circuit related to the colossal dielectric permittivity and varistor properties was proposed, in which a Warburg impedance was added in parallel with the resistance and capacitance.