The electrical and dielectric stability of zinc oxide-based varistors were investigated with the cobalt oxide contents in the range of $0.5~5.0 mol%$. As cobalt oxide contents increased, the ceramic density increased in the range of $5.25~5.55g/cm^3$ and the varistor voltage decreased in the range of $235.3~86.0V$. The varistor with on addition of cobalt oxide $1.0 mol\%$ exhibited good nonlinearity. in which the nonlinear exponent is 66.6 and the leakage current is $1.2{mu}A$. Furthermore, the varistors exhibited the highest electrical and dielectric stability, with $\%{Delta}V_{1mA}=-1.9\%,;\%{Delta}{alpha}=-10.5\%,;\%{Delta}I_L=+275.0\%,;and;\%{Delta}tna{delta}=+55.6\%$, under DC accelerated aging $0.95V_{1mA}/150^{circ}C/24h$.