Our recent studies on current-voltage characteristic and grain boundary structure in ZnO bicrystals are reviewed in this paper. All types of undoped ZnO bicrystals showed Ohmic characteristics. This indicates that nonlinear current-voltage characteristic cannot be generated solely by the atomic disarrangement in undoped ZnO. On the other hand, co-doped ZnO bicrystals showed nonlinear current-voltage characteristics, which depended on the types of grain boundary. It is considered that the nonlinearity depends on the Pr concentrations at the respective grain boundaries.