Resistive random access memory (ReRAM) with conductor-dielectric-conductor structures has attracted extensive attention for next generation nonvolatile memory devices. The resistive switching effect has been observed in various materials, such as metal oxides and chalcogenide oxides. From our findings, we advocate the resistive switching characteristics of zinc oxide thin film, due to its simple composition and ease of manipulation. In this study, we investigated the current-voltage (I-V) characteristics of the Cr/ZnO/Cr capacitor structure. The Cr electrode and ZnO thin film were deposited by radio frequency magnetron sputtering at room temperature. The top electrode layers were patterned by 100 microm x 100 microm. The fabricated devices of the Cr/ZnO/Cr structures exhibited bipolar switching behavior. In addition, using the Cr-coated AFM tip replaced with the top electrode enabled us to map the local current image and measure the current flow at each point. This gave us more information to verify the resistive switching mechanism of ZnO thin film.