Rare-earth oxides are doped into ZnO varistors as grain growth inhibitors for increasing the varistors' voltage gradients. However, their leakage currents become large and their nonlinear coefficients decrease at the same time. The reasonable explanation for such a phenomenon has not yet been available. In this paper, the temperature dependences of varistor samples' leakage currents are investigated, which reveal that the increased leakage currents of ZnO varistors with Y(2)O(3) doping are mainly due to the bypass paths through the intergranular materials at grain corners.