In this study, the third-order nonlinearity and optical bistability effect of mono-layer graphene was investigated. Using theoretical analysis and numerical simulation, the threshold value of the optical bistability of mono-layer third-order nonlinearity graphene can be tuned by changing its Fermi energy, relaxation time, two-photon absorption coefficient, and temperature. We demonstrate that the larger Fermi energy level,the higher temperature and the larger threshold value of the optical bistability. Further, a higher two-photon absorption coefficient corresponds to a higher low threshold of the bistability. Moreover, the relaxation time and two-photon absorption coefficient can significantly alter the light transmissivity of the graphene structure, although the light transmissivity is insensitive to the temperature of the graphene material. Results offer a theoretical basis for designing nanophotonic devices with micro-nano structure such as optical switches and optical sensors.