The electrical characteristics of $ZnO-Pr_6O_{11}-CoO-Cr_2O_3-Y_2O_3$(ZPCCY)-based varistors were investigated with $Y_2O_3$ content in the range of 0.0~4.0 mol%. As $Y_2O_3$ content is increased, the average grain size was markedly decreased in the range of 18.6~3.2 $mu m$ and the density of the ceramic was decreased in the range of 5.53 ~3.74 $g/ extrm{cm}^3$. While, the varistor voltage was increased in the range of 39.4~748.1 V/mm and the nonlinear exponent was in the range of 4.5~51.2 with increasing $Y_2O_3$ content. The addition of $Y_2O_3$ greatly enhanced the nonlinear properties of varistors, compared with the varistor without $Y_2O_3$. In particular, the varistors with $Y_2O_3$content of 0.5 mol% exhibited the highest nonlinearity, in which the nonlinear exponent is 51.2 and the leakage current is 1.3 $mu A$. The donor concentration and the density of interface states were decreased in the range of (4.19~0.14) $ imes$10$^{18}$ /㎤ and (5.38~1.15)${ imes}10^{18}/ extrm{cm}^3$, respectively, with increasing $Y_2O_3$ content.