In this paper, a silver based surface plasmon resonance (SPR) sensor with graphene and dielectric layer was presented. The influences of dielectric layer and graphene on sensitivity and other sensing properties were theoretically calculated and then comprehensively discussed. The refractive index sensitivities for composite silver film based SPR sensors with graphene and dielectric layer could be increased by 29% and 288% than that of monolayer silver film based SPR sensor, respectively. Further, the sensitivity could be enhanced by 202% when combining graphene and dielectric layer together. Considering the high adsorptive capacity of graphene for biochemical molecules, the composite silver film with both dielectric layer and graphene would have great potential application in biochemical sensing fields. Further, BSA protein was successfully used to verify the biochemical sensing ability of proposed SPR sensor. The shift of resonance angle is nearly 3.1 folds than that of monolayer silver based SPR sensor.