A varistic nonlinear I-V characteristic caused by a tunneling effect was observed in two-dimensional nanopolycrystal ZnO (NPC-ZnO) with double Schottky barriers (DSBs). Id-Vd characteristic of a NPC-ZnO field effect transistor showed a negative differential resistance characteristic at room temperature. The Id-Vg showed clear current peaks and valleys although this characteristic has an asymmetric hysteresis. An ultraviolet irradiation on the Id-Vg showed the increase of current peaks and disappearance of the hysteresis. These results could be related to the tunneling effect via DSBs and quasibound states that were caused by the internal defect of ZnO dots or the grain boundary.