The recent discovery of nanoelectronics memristor devices has opened up a new wave of enthusiasm and optimism in revolutionizing electronic circuit design, marking the beginning of new era for the advancement of neuromorphic, high-density logic and memory applications. Here a highly non-linear dynamic response of a bio-memristor is demonstrated using natural silk cocoon fibroin protein of silkworm, Bombyx mori. A film that is transparent across most of the visible spectrum is obtained with the electronic-grade silk fibroin aqueous solution of ca. 2% (wt/v). Bipolar memristive switching is demonstrated; the switching mechanism is confirmed to be the filamentary switching as observed by probing local conduction behavior at nanoscale using scanning tunneling microscopy. The memristive transition is elucidated by a physical model based on the carrier trapping or detrapping in silk fibroin films and this appears to be due to oxidation and reduction procedures, as evidenced from cyclic voltammetry measurements. Hence, silk fibroin protein could be used as a biomaterial for bio-memristor devices for applications in advanced bio-inspired very large scale integration circuit design as well as in biologically inspired synapse links for energy-efficient neuromorphic computing.