LiNbO _3 (LNO) is currently intensively studied as an important ferroelectric material. In this work, polycrystalline LNO films were prepared through a sputtering technique, and their ferroelectricity-related resistive switching property was investigated using a device structure of PtSi/SiO _2 /LNO/Pt. The device exhibits a volatile resistance switching property at lower positive sweeping voltages and a stable bipolar nonvolatile switching property at higher sweeping voltages. The resistive switching mechanism of the device is discussed based on the domain wall conductivity characteristics of the polycrystalline LNO thin films. The PtSi/SiO _2 /LNO/Pt memristor device has potential applications in memory and artificial neural synapses.