A scheme for modulating Kerr nonlinearity and optical bistability (OB) based on a monolayer graphene nanoribbon nanoresonator (NR) and a metallic nanoshell (MNS) is proposed. The MNS is made of an Au nanoshell and a dielectric core. Here, we not only demonstrate that the spectrum of the Kerr coefficient can switch from a four-peaked structure to a two-peaked structure by increasing the shell thickness of the MNS, but also plot bistability phase diagrams in the system’s parameter subspace, revealing that the bistable effect can be controlled vi...