In this study, we have investigated the effects of Co doping on I-V curves, bulk trap levels and grain boundary characteristics of ZnO-$Bi_2O_3$ (ZB) varistor. From I-V characteristics the nonlinear coefficient (a) and the grain boundary resistivity (${ ho}_{gb}$) decreased as 32${ ightarrow}$22 and 18.4${ ightarrow}0.6{ imes}10^9{Omega}cm$ with sintering temperature (900~1,300$^{circ}C$), respectively. Admittance spectra and dielectric functions show two bulk traps of zinc interstitial, $Zn_i^{{cdot}{cdot}}$(0.16~0.18 eV) and oxygen vacancy, $V_o^{{cdot}}$ (0.28~0.33 eV). The barrier of grain boundaries in ZBCo (ZnO-$Bi_2O_3-Co_3O_4$) could be electrochemically single type. However, its thermal stability was slightly disturbed by ambient oxygen because the apparent activation energy of grain boundaries was changed from 0.93 eV at the 460~580 K to 1.13 eV at the 620~700 K. It is revealed that Co dopant in ZB reduced the heterogeneity of the barrier in grain boundaries and stabilized the barrier against the ambient temperature.