Crossbar arrays are the most promising application of a resistive random access memory (RRAM) device for achieving high density memory. However, cross-talk interference in the crossbar array limits the increase in the integration density. In this paper, the combination of two anti-parallel connected diodes and a bipolar RRAM cell is proposed to suppress the sneak current in a crossbar array with anti-parallel connected diodes as the selector for the bipolar RRAM. By using the anti-parallel connected diodes as a selector, the sneak current can be effectively suppressed and the high density crossbar array of more than 1 Mb can be realized as estimated by the 1/2V read voltage scheme. These results indicate that anti-parallel connected diodes can be used as a bipolar selector and have great potential for high density bipolar RRAM crossbar array applications.