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In order to achieve tunable dual Fano resonance effect and high sensitivity refractive index sensing design, an H-shaped waveguide resonator is proposed to couple with the Metal-Dielectric-Metal (MDM) waveguide containing a single metal baffle in the middle part. The transmission spectra of the proposed structure have been calculated through the finite element method. It is demonstrated that double sharp and asymmetric transmittance peaks are emerged at the wavelengths around 810 and 1 350 nm respectively, which are generated by the double Fano resonances occurred vertically and horizontally in the H-shaped resonator with dimension of 300 nm×300 nm. Furthermore, the dependence of the transmission peaks on the structural parameters and refractive index of the H-shaped resonator have been discussed in detail. Finally, the double transmission peaks with the respective sensitivity of 750 and 1 360 nm/RIU have been achieved simultaneously in the proposed structure, which provide guidance for the design of nano-scale biosensors.