In this study, a new plasmonic biosensor is proposed, which is highly sensitive with a compact structure, based on numerical methods for glucose concentration monitoring in different samples. The biosensor is based on a metal-insulator-metal waveguide and a ring resonator, and the calculated results are analyzed. The glucose biosensor operation is based on the refractive index of the glucose solution in the structure. In this study, to improve the sensitivity of the biosensor, the effect of the inner radius size parameter on spectral sensing has been fully analyzed. This biosensor in resonance wavelengths has a linear relationship with the refractive index of the glucose solution. In this structure, the maximum linear sensitivity is in glucose concentration. In addition, compared to other similar sensors, this biosensor has a label-free detection basis and has a very simple and ultra-compact structure: its size is . Considering the special features of this sensor, it could be used as optical on-chip biosensors for glucose concentration monitoring.