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In this study, a novel refractive index sensor structure was designed consisting of a metal-insulator-metal (MIM) waveguide with two rectangular baffles and a U-Shaped Ring Resonator (USRR). The finite element method was used to theoretically investigate the sensor’s transmission characteristics. The simulation results show that Fano resonance is a sharp asymmetric resonance generated by the interaction between the discrete narrow-band mode and the successive wide-band mode. Next, the formation of broadband and narrowband is further studied, and finally the key factors affecting the performance of the sensor are obtained. The best sensitivity of this refractive-index sensor is 2020 nm/RIU and the figure of merit (FOM) is 53.16. The presented sensor has the potential to be useful in nanophotonic sensing applications.