The microstructure and the electrical properties of a ZnO varistor, which was composed of a ZnO-$Bi_2O_3$-$Sb_2O_3$-CoO- $MnO_2$ -NiO-$Nd_2O_3$ system, were investigated at various $Y_2O_3$ addition concentrations. $Y_2O_3$ played a role in the inhibition of the grain growth. As the $Y_2O_3$ content increased, the average grain size decreased from $6.8{mu}m$ to $4{mu}m$, and the varistor voltage($V_{1mA}$) greatly increased from 275 to 400 V/mm. The nonlinearity coefficient ($alpha$) decreased from 72 to 65 with increasing $Y_2O_3$ amount. On the other hand, the leakage current ($I_L$) increased from 0.2 to 0.9 ${mu}A$. These results confirmed that doping the varistors with $Y_2O_3$ is a promising production route for production of a higher fine-grained varistor voltage ($V_{1mA}$) which can dramatically reduce the size of the varistors.