In this study we aims to evaluate the effects of 1/3 mol% $Co_3O_4$ addition on the reaction, microstructure development, resultant electrical properties, and especially the bulk trap and grain boundary properties of $ZnO-Bi_2O_3-Sb_2O_3$ (Sb/Bi=2.0, 1.0, and 0.5) system (ZBS). The samples were prepared by conventional ceramic process, and characterized by XRD, density, SEM, I-V, impedance and modulus spectroscopy (IS & MS) measurement. In addition of $Co_3O_4$ in $ZnO-Bi_2O_3-Sb_2O_3$ (ZBSCo), the phase development, density, and microstructure were controlled by Sb/Bi ratio. Pyrochlore on cooling was reproduced in all systems. The more homogeneous microstructure was obtained in ZBSCo (Sb/Bi=1.0) system. In ZBSCo, the varistor characteristics were improved drastically (non-linear coefficient ${alpha}$=23~50) compared to ZBS. Doping of $Co_3O_4$ to ZBS seemed to form $V^{cdot}_o$(0.33 eV) as dominant defect. From IS & MS, especially the grain boundary of Sb/Bi=0.5 system is composed of electrically single barrier (0.93 eV) and somewhat sensitive to ambient oxygen with temperature.