In order to realize tunable multichannel high sensitivity refractive index sensing, a square resonator connected with a Rectangular Groove (RG) is proposed to couple with the highly compact Metal-Dielectric-Metal (MDM) waveguide containing double metal baffles. The transmission spectrums of the proposed waveguide structure have been calculated by the finite element method, which exhibits four sharp, asymmetric transmittance peaks and the magnetic field patterns. Based on the coupling interference between the broadband reflection mode generated by the double baffles and the narrow resonance modes occurred in the composite cavity, the generation mechanism of quadruple Fano resonance is explained. Moreover, the structural parameters of the square cavity and the rectangular groove are changed to study the tunability of the wavelengths of the quadruple transmittance peaks. When the composite cavity is filled with different dielectric media, the calculated sensitivity corresponding to four transmittance peaks are 960, 1 120, 1 320 and 1 560 nm/RIU, respectively. It provides an effective theoretical reference for the design of multi-channel and high sensitivity refractive index sensor.