Highly (002)-oriented and columnar-grained ZnO thin films were prepared by radio frequency magnetron sputtering at room temperature. The $\mathrm{Pt}∕\mathrm{Zn}\mathrm{O}∕\mathrm{Pt}$ devices exhibit reversible and steady bistable resistance switching behaviors with a narrow dispersion of the resistance states and switching voltage. Only a low forming electric field was required to induce the resistive switching characteristics. The resistance ratios of high resistance state to low resistance state were in the range of 3–4 orders of magnitude within $100\text{cycles}$ of test. It was also found that the conduction mechanisms dominating the low and high resistance states are Ohmic behavior and Poole-Frenkel emission, respectively.