In recent years, various nanostructures related to Fano resonance have been proposed by many researchers due to their outstanding optical properties. A structure consisting of two double-split rings (TD-SR) is researched by using finite element method in this paper. When the incident light is normal to the structure surface, a magnetic Fano resonance can be generated by the interference of bright electric mode and dark magnetic mode. In addition, when the symmetry of the structure is destroyed along x-axis or y-axis, double Fano resonances will be generated. At the same time, the maximum refractive index sensitivity (S) and the maximum figure of merit at resonance mode can reach 1200 nm/RIU and 30.61, respectively. More interestingly, the electromagnetically induced transparency (EIT)-like behavior can be induced when the cavity of inner split ring is biased and the corresponding electric and magnetic field enhancements can reach 229 and 52, respectively. The optical properties of our nanostructure make it has important application value in the fields of multi-wavelength sensor, ultra-sensitive biosensor, surface enhanced spectroscopy and slow light.