In this paper, a plasmonic refractive index sensor based on metal insulated metal waveguide (MIM) with three rings and a resonant cavity is first proposed and numerically evaluated. Next, we add four teeth to the sensor structure. We study and simulate the resonant wavelengths and refractive index of resonators using the time difference finite difference method. Given that the sensor and the conduction characteristics of plasmonic waves are influenced by the structure parameters,Therefore, by changing the refractive index and changing the dimensions and coordinates of the cavity and rims, we can change the passage coefficient in the resonant modes and measure the sensor performance. As a result, we obtain the sensitivity coefficient, the figure of merit (FOM) and the quality factor Q of the sensor. We modulate the resonance wavelength FWHM using the generated modes and reach a sensitivity of 2166 nm / RIU. These plasmonic sensors with a simple framework and balanced performance and high optical resolution can be used to measure the refractive index in the medical, chemical and food industries.