Resistance random access memory is regarded as one of the most promising candidates for the future nonvolatile memory applications due to its good endurance, high storage density, fast erase speed and low power consumption. As one of the most important transition-metal oxides, the anatase TiO2 has received intense attention due to its inexpensive cost, strong optical absorption, favorable band edge positions and superior chemical stability. In the last decade, the nanometer-sized TiO2 has been shown to exhibit a wide range of electrical and optical properties, such as nanoscale electronics and optoelectronics, which rely mainly on the unique size and shape. Recently, various anatase TiO2 based devices such as the anatase TiO2 nanotube based memristor and the anatase TiO2 nano-film based memristor have been intensively studied due to their nonvolatile resistive switching performances. Furthermore, many conduction mechanisms have been used to elucidate the resistive switching behaviors of the anatase TiO2 based devices. However, the direct growth of anatase TiO2 nanowire arrays (NWAs) on the FTO substrate is still a challenge since there exists a large lattice mismatch of about 19% between the anatase TiO2 NWAs and the FTO substrate. Moreover, the Au/TiO2/FTO based device has not been reported and the resistive switching mechanism of the anatase TiO2 NWAs based memristor is still unclear. In this work, the anatase TiO2 NWAs with (101) preferred orientation are successfully grown on the FTO substrate by a facile one-step hydrothermal process. The resistive switching characteristics and resistive switching mechanism of the as-fabricated Au/TiO2/FTO memristor are investigated systemically. The result indicates that the Au/TiO2/FTO memristor exhibits nonvolatile bipolar resistive switching behavior. Meanwhile, the resistance ratio between high resistance state and low resistance state exceeds 20 at 0.1 V, which can be maintained over 103 s without significant degradation. In addition, the conduction mechanism of the low resistance state is governed by the ohmic conduction mechanism, while the trap-controlled space charge limited current conduction mechanism dominates the high resistance state. The resistive switching model of the Au/TiO2/FTO memristor is developed, and the resistive switching mechanism could be attributed to the formation and rupture of the conductive filaments relating to the localized oxygen vacancies. It demonstrates that the Au/TiO2/FTO memristor may be a potential candidate for the future nonvolatile memory applications.