In order to achieve a compact structure to realize the refractive index sensor with high Figure of Merit (FOM) in a nanometer scale, a Metal-Dielectric-Metal (MDM) waveguide containing a metallic baffle side-coupled to U-shaped resonator is proposed to produce sharp and asymmetric Fano resonance. The asymmetric response line-shape of the Fano resonance is formed by the destructive interference between the wide continuous state generated by the single metallic baffle and the narrow discrete state excited by U-shaped resonator. The transmission properties of the proposed structure are numerically calculated by the finite element method, and the influence of structural parameters on the transmission spectrum and the value of FOM are analyzed quantitatively. The simulation results after parameter sweeping reveal that the FOM value of the optimized structure can attain to 47 382 and the sensitivity of resonant wavelength with refractive index drift is 800 nm/RIU. The waveguide structure can provide effective references for the design of nano-scale refractive index sensor.