Surface Plasma resonance (SPR) sensors combined with biological receptors are widely used in biosensors. Due to limitations of measurement techniques, small-scale, low accuracy, and sensitivity to the refractive index of solution in traditional SPR prism sensor arise. As a consequence, it is difficult to launch commercial production of SPR sensors. The theory of localized surface plasmon resonance (LSPR) developed based on SPR theory has stronger coupling ability to near-field photons. Based on the LSPR sensing theory, we propose a submicron-sized golden-disk and graphene composite structure. By varying the thickness and diameter of the array disk, the performance of the LSPR sensor can be optimized. A graphene layer sandwiched between the golden-disk and the silver film can prevent the latter from oxidizing. Symmetrical design enables high-low concentration of dual-channel distributed sensing. As the fixed light source, we use a 632.8-nm laser. A golden nano-disk with 45 nm thickness and 70 nm radius is designed, using a finite difference time domain (FDTD) simulation system. When the incident angle is 42°, the figure of merit (FOM) reaches 8826, and the measurable refractive index range reaches 0.2317.