Optical switches based on plasmonic nanostructures are of great interest due to their high speed performance. To improve the broadband switching performance, a plasmonic design based on metal-insulator-metal (MIM) structure and monolayer graphene (as an active layer) is proposed. In this scheme, the light absorption of the monolayer graphene and the optical bandwidth are increased due to magnetic dipole resonance and magnetic coupling effect. The numerical simulation results of the proposed structure reveal that high absorption is achieved at the wavelength of 1.55 μm which is 67% and 93% for the monolayer graphene and the whole structure, respectively. This structure has a high absorption modulation depth which can be reached nearly 100% around the interband transition position in a wide wavelength range from 1 μm to 2.5 μm. Also, regarding its short response time of 10 fs, this structure can be used as an ultrafast switch. In addition, the equivalent circuit model of the structure is derived from the transmission line model (TLM) that its results are in a very good agreement with the numerical simulation results.