We demonstrate that a bipolar non-volatile resistive switching behaviour with negative differential resistance (NDR) effect is realized in a Cu/BaTiO₃/Ag device, which was deposited on a Si substrate via magnetron sputtering equipment. We suggest that the bipolar resistive switching is dominated by the trapping/detrapping of electrons at the BaTiO₃–Cu interface. In addition, we demonstrate that the device exhibits good performance, including a large on/off ratio, high reliability and long retention time. Therefore, BaTiO₃ may become a good candidate for application in resistive switching random access memory (RRAM) devices.