ZnO Varistor is an electronic ceramic device to absorb the surge voltage from low voltage to high. To investigate the puncture mechanism occurring in NnO varistor, the Voronoi simulation for formulating the relation between the applied voltage and the increase of the temperature inside grain is applied. The Voronoi network can realize the structure of the practical varistor better than the established simple network. Using the current through each grain and the voltage applied to the grain, Joule heating energy is calculated and the phenomenon that the puncture occurs can be analyzed quantitatively by simulating the electric and thermal characteristics according to the externally applied pulsed voltage.