A metal-dielectric-metal (MDM) waveguide coupling two square cavities with double baffles is designed in this paper based on the transmission characteristics of surface plasmon polaritons in subwavelength structure. The independent tuning of the dual Fano resonance is implemented by the interference between the wide-spectrum mode generated by the F-P (Fabry Perot) cavity and the two narrow-spectrum modes generated by the two square cavities. Moreover, the independent tuning of the dual Fano resonance can be achieved by changing the sizes of the two square cavities and filling medium. The coupled-mode theory (CMT) is adopted to analyze the transmission characteristics of the dual Fano resonance. The structure is simulated by the finite element method to quantitatively analyze the influence of structural parameters on the independent tuning of the dual Fano resonance and the refractive index sensing characteristics. The proposed sensor yields respectively sensitivity higher than 1020 nm/RIU and 1120 nm/RIU and a figure of merit of 3.29 × 10⁵ and 1.17 × 10⁶ by optimizing the geometry parameters. This structure provides an effective theoretical reference in the optical integration of ultra-fast optical switches, multi-function high-sensitivity sensors and slow-light devices.