A novel nanostructure based on a simple metal-dielectric-metal (MDM) bus waveguide with sliver baffle as well as an E-shaped cavity is proposed to generate double Fano resonances arising from interference between broad continuous state and narrow discrete state. The commercial software COMSOL based on finite element methods is used to explore the Fano resonances properties and the senor properties of the system. According to the simulation results, it is demonstrated that E-shaped cavity can generate two discrete states, and the continuous sate is constructed by loading sliver baffle in bus waveguide. Moreover, it can be found that the Fano peak wavelengths and profiles can easily be tuned via structural parameters. Interestingly, the independent control of the left Fano resonance (LFR) can be accomplished by changing horizontal cavity length of E-shaped cavity. Meanwhile, our proposed nanostructure has a higher sensitivity of 1 440 nm/RIU as well as a higher figure of merit (FOM) value approximately 5 244. In conclusion, the proposed independently tunable Fano nanostructure may have a great promising in the fields of nanosensors, filters and other optical devices.