We report the application of nanodiamond prepared by microwave plasma chemical deposition system as the dielectric film with copper as top electrodes and a tungsten counter electrode for the fabrication of resistive random access memory (RRAM). The RRAM is switched between the high-resistivity state and a low-resistivity state of nanodiamond film. The high or low resistance state can be probed by applying a low voltage across two counter electrodes on two sides of the nanodiamond film and measuring its conduction current. We observed that the Cu/Nanodiamond/W structure shows good performance with ON/OFF current ratio >105 and retention time >104 s. Nanodiamond is known to be chemically inert, good for heat dissipation, and has very low solid solubility in copper. It is, therefore, a suitable dielectric material for RRAM for harsh environments.