The speed with which electronic products are updated is continuously increasing. Consequently, since waste electronic products can cause serious environmental pollution, the demand for electronic products made of biological materials is becoming increasingly urgent. Although biological memristors have significant advantages, their electrical characteristics still do not meet the requirements to be used in future nonvolatile memories. Therefore, how to control their electrical characteristics has become a popular topic of research. In this study, tunable biomemristors with an Al/tussah blood (TB)-carbon nanotube (CNT)/indium tin oxide (ITO)/glass structure were fabricated. Such a device exhibits stable bipolar resistance switching behavior and good retention characteristics (104 s). Experimental results show that the ON/OFF current ratio can be effectively controlled by modifying the CNT concentration in the TB-CNT composite film. Multilevel (8 levels, 3 bits per cell) storage capabilities can be achieved in the device by controlling its compliance current in order to achieve high-density storage. The resistance switching behavior originates from the formation and rupture of conductive oxygen vacancy filaments. TB is a promising natural biomaterial in the field of green electronics, and this research could blaze a new trail for the development of biological memory devices. Biomemristors with multilevel resistance states can be used as electronic synapses and are one of the choices for simulating biological synapses.