A plasmonic refractive index sensor including a Metal-Insulator-Metal waveguide (MIM) with four teeth is proposed. Transmittance (T), Sensitivity (S) and Figure of Merit (FOM) investigated numerically and analysed via Finite Difference Time Domain method (FDTD). The simulation results show the generation of double Fano resonances in the system that the resonance wavelength and the resonance line-shapes can be adjusted by changing the geometry of the device. By optimizing the structure in the initial configuration, the maximum sensitivity of 1078nm/RIU and FOM of 3.62×105 is achieved. Then change the structure parameters. In this case, the maximum sensitivity and FOM are 1041nm/RIU and 2.94×104 respectively, thus two detection points can be used for the refractive index sensor. Due to proper performance and adjustable Fano resonance points, this structure is significant for fabricating sensitive refractive index sensor and plasmonic bandpass filter.