Surface Plasmon’s in graphene have been used extensively due to their extraordinary specifications. In this paper, surface Plasmon’s were formed in the near infrared region using steps gold grating covered by a graphene monolayer and a sensitive layer structure. also the optical properties of the graphene and the extinction of the structure was studied. By using the wavelength dependence of the Plasmon’s resonance on the optical properties of sensitive layer, a gas sensor in near infrared were suggested. By introducing the sensitivity coefficient of S = ?? /?n, and the quality factor Q=S/FWHM the with change in refractive index from n=1.000 to n=1.100 and ?n=0.005 sensitivity of the structure for gasses was calculated. It was also observed that this structure shows the highest sensitivity for the refractive indexes n = 1.020 with S=1600 nm/RIU and the highest quality factor Q=333.3 1/RIU is for n=1.010, n=1.030, n=1.085 in near infrared region.