Surface Plasmon’s in graphene have been used extensively due to their extraordinary specifications. In this paper, surface Plasmon’s in visible and near infrared regions using a photonics crystal of gold nanoribbons in the vicinity of graphene was constructed and the optical properties of the graphene and the 1-R of the structure was studied. We have studied, the wavelength dependence of the Plasmon’s resonance on the optical properties of the structure including the refractive index of the detected material. By introducing the sensitivity coefficient of S = Δλ /Δn, the sensitivity of the structure to the partial changes of the refractive index was calculated. It was also observed that this structure shows the highest sensitivity for the refractive indexes n = 2 to n = 3 with approx. 300 nm/RIU in the visible and infrared region.