In this study, carbon fibers (Cf) coated with Ba0.6Sr0.4TiO3 (BST) ([email protected]f) were prepared by magnetron sputtering and subsequently heated in nitrogen to produce oxygen vacancies. [email protected]f and nitrogen-treated [email protected]f were cross-stacked on polyimide (PI) film to make a [email protected]f memristor. The electrical properties of [email protected]f memristor were measured after being bent 3000 times. The device exhibits bipolar figure-of-eight (f8) hysteresis loop characteristics under applied voltage. The hysteresis loops narrow with increasing temperature of heat treatment in nitrogen, due to decrease in oxygen vacancy concentration. The hysteresis loops demonstrate the switching process of resistance between high resistance state (HRS) and low resistance state (LRS), with a maximum HRS/LRS ratio of 106. The switching process can be divided into two parts, corresponding to Schottky Emission and Fowler-Nordheim (F–N) Tunneling. It is notable that no electroforming voltage is required to stimulate the memristor. The constructed memristor was cycled successfully 1000 times and retained the LRS 787 s during power cut off. In addition, the device exhibited synaptic behavior including learning and forgetting processes, in accordance with the paired-pulse facilitation (PPF) rule. The use of [email protected]f in the construction of the nonvolatile memristor imparts flexibility to the device allowing for the possibility of wearable flexible intelligent memristor based electronic devices in the future.