We numerically investigate the optical bistability effect in the metal-insulator-metal waveguide with a nanodisk resonator containing a Kerr nonlinear medium. It is found that the increase of the refractive index, which is induced by enhancing the incident intensity, can cause a redshift for the resonance wavelength. The local resonant field excited in the nanodisk cavity can significantly increase the Kerr nonlinear effect. In addition, an obvious bistability loop is observed in the proposed structure. This nonlinear structure can find important applications for all-optical switching in highly integrated optical circuits.