A graphene/Ag structure is engineered as an enhanced platform for surface plasmon resonance sensing due to the high impermeability nature of graphene and the superior surface plasmon resonance performance of Ag. This structure is ultrasensitive to even tiny refractive index change of analytes based on Goos-Hänchen shift measurement compared to the traditional SPR sensor with bare Au film. The graphene/Ag configuration is consisted of five components, including BK7 glass slide, titanium thin film, silver thin film, two-dimensional graphene layers and biomolecular analyte layer. We have optimized the parameters of each layer and theoretically analyzed Goos-Hänchen shift of the plasmonic structure under surface plasmon resonance effect. The optimized graphene/Ag structure is monolayer graphene coated on Ag thin film with the thickness of 42 nm.