Surface plasmon resonance (SPR) is a rapid and sensitive technique used for probing the biomolecular interactions in real time. Several new approaches have been suggested to improve the sensitivity of SPR sensors over the last two decades. Most of them are based on creating or patterning nanostructures/nanomaterials in order to enhance the sensitivity. Graphene offers several advantages due to its special optical and structural properties. Herein, we propose a new angular interrogated dual wavelength based differential detection approach for graphene based SPR sensing to increase the sensitivity. Reflectivity of the p-polarized incident light has been calculated using the N-layer model for the most common Kretschmann configuration. Sensitivity of the SPR with and without graphene layers has been calculated for single and dual wavelength based approaches. Computational results show that the proposed graphene SPR sensor has (1 + 0.4 L) η times higher sensitivity than the conventional gold thin film based SPR sensors. Further, increasing the number of graphene layers, L, improves the sensitivity. Where, η represents the enhanced sensitivity due to increased binding/adsorption of biomolecules on graphene over a gold thin film. Sensitivity analysis has been carried out for a refractive index (Δn) = 0.005 with L = 1 to 10.