Local surface plasmon resonance is a kind of resonance phenomenon caused by collective oscillation of free electrons on the surface of metal nanoparticles under the action of photons. A kind of square and ring/disk array structure is proposed in this paper, which is composed of the left single ring, the right square and the eccentric ring disk. The optical properties of the structure are investigated by the finite difference time domain (FDTD) method. Fano resonances appear in the transmission spectra due to the electric field couplings between the arrays when linearly polarized light is incident to the metal surface. Obvious resonant valley characteristics are formed at different positions in the wavelength range of 600～1 700 nm. Comparison and analysis of electric field and charge simulation diagram, it is found Fano resonance is formed by the coherent interference between the dipole resonance of the ring and the four dipole resonance modes excited by the square and the ring/disk. The local surface plasmon resonance between metal nanoparticles changed by the coupling effect of the electric field. Therefore, the Fano resonance is dependent on the parameters of the structure (such as the diameter of the left ring L, the diameter of the right ring R, the height of the structure H, the distance from the left ring to the square D, etc. ). By changing the parameters of the structure, the wavelength position and the resonant intensity of the resonant valley can be effectively controlled and the optical properties also can be controlled. Because of the unique asymmetry of the structure, the influence of the polarization direction of the incident light source (the angle between the electric vector and the x axis) on the position of the resonant valley wavelength and the resonant intensity of the structure is further investigated. The structure shows that with the increase of the polarization angle of the light source, the wavelength position at the resonant valley J2 appears obvious red shift phenomenon. However, when the polarization angle is 90°, the Fano resonance can not occur at the resonance valley J3. Therefore, the resonant intensity and the resonant wavelength position of the structure can be controlled by changing the polarization direction of the light source. More importantly, the structure has a high sensitivity to the environmental refractive index, up to 755 nm·RIU-1, and the figure of merit (FOM) can reach 18.4. The results show that the structure has potential application prospects in the applications of environmental refractive index sensors and micro-nanophotonic devices.