The electrical properties and dc aging behavior for specified stress state of system, which is composed of quaternary Zn-Pr-Co-Cr, were investigated for different $Dy_2O_3$ addition doping level. As $Dy_2O_3$ doping level increased, the density decreased in the range of 5.51-4.90 $g/cm^3$, reaching maximum at 0.5 mol% and the average ZnO grain size decreased in the range of 17.7-6.0 ${mu}m$. The incorporation of $Dy_2O_3$ significantly improved the non-ohmic properties, above 30 in non-ohmic coefficient, compared with that of undoped samples. The samples with the best performance of non-ohmic properties were obtained for $Dy_2O_3$ doping level of 1.0 mol%, with 49 in non-ohmic coefficient and 2.6 ${mu}A/cm^2$ in leakage current. The samples with the highest stability were obtained for $Dy_2O_3$ doping level of 0.5 mol%.