Through injecting 8/20 and 30/60 μs impulse currents to five kinds of ZnO varistors, the influence of the varistor size on the single impulse current withstanding capability of a ZnO varistor is investigated in this article. A comprehensive damage criterion of a varistor consisting of three aspects, namely, mechanical failure by visual inspection, abnormal saltation in voltage or current waveform, and over 5% variation in reference voltage or leakage current >50 μA is proposed here. The diameters of the ZnO varistor under test vary from 42 mm to 60 mm, and the heights vary from 22 mm to 31 mm. The obtained results show that, under the same impulse current waveform, the mean voltage and the mean energy density of ZnO varistor increase approximately, proportionally with increasing amplitude of impulse current density. Besides, the voltage withstanding capability per unit height of varistor varies from 4.408 to 4.940 kV/cm under 8/20 μs impulse current, and from 4.256 to 5.148 kV/cm under 30/60 μs impulse current. The current withstanding capability per unit area of the varistor varies from 2.134 to 3.842 kA/cm2 under 8/20 μs impulse current, and from 1.738 to 3.490 kA/cm2 under 30/60 μs impulse current. Moreover, the energy withstanding capability per unit volume of the varistor ranges from 206 to 421 J/cm3 under 8/20 μs impulse current, and from 311 to 752 J/cm3 under 30/60 μs impulse current. Furthermore, due to the fact that nonuniformity of the polycrystalline‐sintered body of ZnO varistors increases with the increasing varistor area, the normalized parameters, including the mean failure voltage, the failure current density, and the failure energy density, decrease with increasing varistor diameters. The normalized parameters proposed here are more effective ones to consider the effect of sizes on the withstanding capacity than the failure current, the failure voltage, and the failure energy. © 2019 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.