We report the bistability of second- and third-harmonic generation in monolayer graphene plasmonics supported by graphene nanoribbon arrays. The nonlinear optical bistability of harmonic generation at the ultra-low threshold intensity ∼100kW/cm2, along with the traditional linear optical bistability of transmittance, is observed due to the different local fundamental fields at the lower and higher state when the Kerr effect of graphene is considered. Importantly, the working fundamental wavelength can be tuned by the Fermi level of graphene and geometrical structure, which leads to the linear and nonlinear optical bistability available in a broadband for potential applications in advanced all-optical devices.