We propose a new model which enables us to explain the highly nonohmic varistor behavior, C-V characteristic, and the role of CoO additive: In the new model, the highly nonohmic varistor conduction process is associated with the hole diffusion current due to the gradient of the holes in ZnO grain, which may be caused by moving holes to the depletion region of the forward biased Schottky barrier from the depletion region of the reverse biased Schottky barrier by tunneling process. As this hole diffusion current is strongly limited by the electron-hole generation rate, it is necessary to increase the electron-hole generation rate for the enhancement of the nonlinearity in I-V characteristic of ZnO varistor. Co ions do this role, i.e., the electron-hole generation rate is increased with CoO concentration in ZnO varistor.