Three samples of ZnO doped with CuO as additive were prepared by solid state reaction from the calcined oxides and characterized by SEM, EDX, and AFM. The results revealed the presence of intergranular phase. Additives found to be between ZnO grains. The conductivity of the three samples was measured with the frequency up to 100 KHz by LCR circuit. The calculated coefficients of nonlinearity and the conductivity are shown to be highly dependent on the frequency, concentration of copper oxide, surface morphology, and microstructure of the varistor samples. The temperature dependence of the conductivity of these samples will be studied in the future work.