Resistive random access memory (RRAM) has been developed as a promising non-volatile memory on plastic substrates for flexible electronic systems owing to its advantages of simple structure and low temperature process. Memory plays an important role in electronic systems for data processing, information storage, and communication, thus flexible memory is an indispensable element to implement flexible electronics. However, cell-to-cell interference existing in a flexible memory array leads to not only undesired power consumption but also a misreading problem, which has been a big hindrance for practical flexible memory application. This paper describes the development of a fully functional flexible one diode–one resistor RRAM device. By integrating high-performance single crystal silicon diodes with plasma-oxidized resistive memory, cell-to-cell interference between adjacent memory cells is effectively prevented, and random access operation of the 1D–1R flexible memory device is successfully achieved on a flexible substrate. The work presented here could provide a useful methodology to realize flexible non-volatile memory with high packing density for flexible electronic applications.