We design a D-shaped fiber optic biosensor based on the surface plasmon resonance (SPR) of a metalgraphene layer and simulate this SPR using the finite element method. Using a metal-graphene layer as the sensing material, surface plasma resonance is simulated as the refractive index of the external environment ranges from 1.33 to 1.36. Simulation results show that a metal-graphene layer attached to the D-shaped optical fiber core can couple with light under a specific polarization state and excite strong plasma oscillations on the layer surface. Calculated transmission coefficients show that the resonance wavelength obviously moves toward longer wavelengths as the refractive index of the test medium increases, and a sensitivity of 5400 nm/RIU is obtained. Because of its large surface volume ratio and good biocompatibility, graphene may be utilized in many applications in the field of biosensing.