As an emerging micro/nano device, memristor integrates functions, such as memory, sensing, and computing, and has similar internal dynamics to synapses, showing great potential in neuromorphic computing and logical operations. In this work, a flexible memristor with Al/TiOx/Al/polyethylene terephthalate structure was developed to investigate the synergistic effect from the oxygen vacancy, H2O molecule, and NaCl. A forming-free resistive switching (RS) behavior observed in the flexible memristor can be ascribed to the migration and accumulation of the oxygen vacancy and Schottky emission of the interfaces. This forming-free RS is sensitive to the NaCl and H2O molecule because the Na+ migration disturbs the oxygen vacancy filament and interplay between oxygen vacancy and H2O molecules. The variation conductance modulated by the concentration of NaCl and H2O molecules can represent the weight update incrementally that the online learning required. Therefore, the memristor has the potential to be used as a biosensor in human tissues or to realize the brain-like chip, which points out the research direction for the extension function of the memristor in wearable systems.