A coupling structure which consists of a metal-insulator-metal resonator centered off from the metal square core and two side-coupled waveguides is designed. The propagation characteristics of the structure are studied by finite element method. The results show that the Fano resonance can be obtained and modulated by adjusting the deviation angle and deviation distance of the metal core in the cavity. The Fano resonance is caused by the symmetry breaking or geometric effect, which affects the intensity of the field distribution in the coupling region between the left and right waveguides and the cavity. The variation of field distribution mode is caused by the interference between the waveguide mode and the cavity mode. In addition, the spectral position and modulation depth of Fano resonance are very sensitive to the deviation parameters. By calculating the refractive index sensing characteristics under different deviation angles and deviation distances, the refractive index sensitivity is up to 1 508 nm/RIU, and the quality factor is up to 1 308. The research results provide a theoretical basis for designing more flexible, simple and efficient on-chip plasmonic nanosensors.