Two structures of graphene-silver asymmetric grating surface plasmon resonance sensors with high sensitivity were presented. In Structure 1, the air, with a thickness of 100 nm, was located on the sensing medium; while, Structure 2 has become small with ignoring the air. The sensitivity of both sensors was calculated through the alteration of the wavelength peak of the extinction curve in minor variability of refractive index of the sensing medium. The sensitivity of Structure 1 and Structure 2 was 880 nm/RIU and 1742 nm/RIU, respectively. By comparing the different sensors, it should be noted that the ability to reach a small-sized sensor with a high performance (Structure 2) is the center of researchers' attention. Also, these two SPR sensors could detect most gases with a refractive index from 1.000 to 1.500 such as CO2, CS2, SO2, and so on, with high precision.