Due to the emergent need of identifying biomolecules at very low densities to diagnose illnesses, as well as detect dangerous gases for health, early on, designing a high-quality sensor with simple structure is one of the most important targets for the researchers. Because of this issue, a graphene-gold grating surface plasmon resonance (SPR) sensor with excellent performance has been proposed. The sensitivity of the proposed sensor is calculated by the wavelength peak shift of the extinction curve, which is due to changes in the refractive index of the sensing medium which are, in turn, due to changes in the density of the identified molecule. Two modes of plasmon have been created in the near-infrared region, and both of them had very good characteristics, including sensitivity and high quality. By optimizing the structure and characteristics of the incident light beam, the highest sensitivity1100nm/RIUandthe qualityfactor3929for thefirst mode(mode 1)and thenotable sensitivity1180nm/ RIU and the quality factor 9833 were obtained for the second mode (mode 2). The label-free SPR proposed sensor can, by measuring the refractive index, detect changes in the concentration of a wide range of materials including gases such as most alloys, and biomolecules such as hemoglobin, breast cancer, and leukemia, and generally materials with a refractive index from 1.000 to 1.600, up to a precision of 0.0001.