As part of an effort to develop low-voltage surge filters, zinc oxide (ZnO) bicrystals were investigated to clarify the electronic state of grain boundaries in ZnO varistors. The varistors had a ZnO/glass/ZnO-type sandwich structure, and the interfacial glass layer was composed of oxide glass of the Bi-B-O system. A highly nonlinear current-voltage relationship was obtained for a sandwich structure composed of Co-doped single crystal ZnO, and the current through the junction was proportional to roughly the 30th power of the bias voltage at the breakdown stage. In contrast, the junction using undoped single crystal ZnO showed insignificant nonlinearity. Dielectric measurements revealed that a double-sided depletion layer was formed at the interface and the high nonlinearity was ascribed to the corresponding potential barrier formed at the interface.