In this work, memristors based on TiO2 nanorod arrays (TNAs) were fabricated using a hydrothermal synthesis method. The memristors had a structure consisting of a TNA sandwiched between gold and fluorine doped fin oxide (FTO) coated glass. Devices were constructed using TNAs containing nanorods of different height, diameter and area ratio, with different oxygen vacancy concentrations. The devices exhibit resistance switching behavior and the current through the devices is related to the oxygen vacancy concentration and the area ratio of TNAs. When the height of nanorods is around 3 mu m or less, the devices perform well with a current that is as low as 10(-8) A in the high resistance state (HRS) and 10(-4) A in the low resistance state (LRS). It is found that the space charge limited current (SCLC) mechanism associated with the oxygen vacancies explains the current-voltage behavior of these devices in this three layer structure. A schematic model is presented to illustrate the changes in oxygen vacancy concentration and switching processes, including the formation of new oxygen vacancies (triggered vacancies) to explain the large increase in current at the end of the setting process in these devices.