The ac response of ZnO-based varistors was measured as a function of temperature and applied electric field. Conductivity-frequency measurements indicated that the grain boundaries of the ZnO varistors were amorphous. The device resistance was found to decrease as the temperature/applied field increased. This was attributed to deterioration of the insulating property of the grain boundaries due to generation of conduction carriers in the ZnO grains. As a large amount of these charge carriers passed through the grain boundaries, the ZnO varistors remarkably revealed a non-Debye characteristic that can be modeled by a capacitance to simulate the behavior of the grain boundaries.