Graphene has exceptional mechanical and electronic properties(1-3), but its hydrophobic nature is a disadvantage in biologically related applications(4,5). Amyloid fibrils are naturally occurring protein aggregates that are stable in solution or under highly hydrated conditions, have well-organized supramolecular structures and outstanding strength(6,7). Here, we show that graphene and amyloid fibrils can be combined to create a new class of biodegradable composite materials with adaptable properties. This new composite material is inexpensive, highly conductive and can be degraded by enzymes. Furthermore, it can reversibly change shape in response to variations in humidity, and can be used in the design of biosensors for quantifying the activity of enzymes. The properties of the composite can be fine-tuned by changing the graphene-to-amyloid ratio.