Herein, we design a high sensitivity with a multi-mode plasmonic sensor based on the square ring-shaped resonators containing silver nanorods together with a metal–insulator-metal bus waveguide. The finite element method can analyze the structure's transmittance properties and electromagnetic field distributions in detail. Results show that the coupling effect between the bus waveguide and the side-coupled resonator can enhance by generating gap plasmon resonance among the silver nanorods, increasing the cavity plasmon mode in the resonator. The suggested structure obtained a relatively high sensitivity and acceptable figure of merit and quality factor of about 2473 nm/RIU (refractive index unit), 34.18 1/RIU, and 56.35, respectively. Thus, the plasmonic sensor is ideal for lab-on-chip in gas and biochemical analysis and can significantly enhance the sensitivity by 177% compared to the regular one. Furthermore, the designed structure can apply in nanophotonic devices, and the range of the detected refractive index is suitable for gases and fluids (e.g., gas, isopropanol, optical oil, and glucose solution).