In this study, we have investigated the effects of Mn and Co co-doping on defects, J-E curves and grain boundary characteristics of ZnO-$Bi_2O_3$ (ZB) varistor. Admittance spectra and dielectric functions show two bulk defects of $Zn_i^{{cdot}{cdot}}$ (0.17~0.18 eV) and $V_o^{cdot}$ (0.30~0.33 eV). From J-E characteristics the nonlinear coefficient (${alpha}$) and resistivity (${ ho}_{gb}$) of pre-breakdown region decreased as 30 to 24 and 5.1 to 0.08 $G{Omega}cm$ with sintering temperature, respectively. The double Schottky barrier of grain boundaries in ZB(MCo) ($ZnO-Bi_2O_3-Mn_3O_4-Co_3O_4$) 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 0.64 eV at lower temperature to 1.06 eV at higher temperature. It was revealed that a co-doping of Mn and Co in ZB reduced the heterogeneity of the barrier in grain boundaries and stabilized the barrier against an ambient temperature (${alpha}$-factor= 0.136).