Plasmon-based sensing relies on the interaction of photons with nanostructured materials. Surface plasmon resonance (SPR) biological and chemical sensors offer unique advantages of real-time and label-free detection techniques and therefore, they have been around in the commercial market for many decades. The principle of the Goos–Hanchen (GH) shift, whereby linearly polarized light undergoes a small lateral shift upon total internal reflection at a dielectric surface, is highly sensitive to refractive index (RI) changes in the sensing medium and can thus be utilized for plasmonic sensing. 2D materials such as graphene can boost the plasmonic efficiency of these sensors because of their excellent optical properties. Herein, a customized GH shift–based SPR sensor is devised using graphene-coated Au chips. With the help of experimental results, it is shown that graphene can enhance the sensitivity of the conventional Au-only configuration 2.35 times.