The demand for flexible electronic systems such as wearable computers, E-paper, and flexible displays has recently increased due to their advantages over present rigid electronic systems. Flexible memory is an essential part of electronic systems for data processing, storage, and communication and thus a key element to realize such flexible electronic systems. Although several emerging memory technologies, including resistive switching memory, have been proposed, the cell-to-cell interference issue has to be overcome for flexible and high performance nonvolatile memory applications. This paper describes the development of NOR type flexible resistive random access memory (RRAM) with a one transistor-one memristor structure (1T-1M). By integration of a high-performance single crystal silicon transistor with a titanium oxide based memristor, random access to memory cells on flexible substrates was achieved without any electrical interference from adjacent cells. The work presented here can provide a new approach to high-performance nonvolatile memory for flexible electronic applications.