In this paper, an asymmetric plasmonic structure composed of a MIM (metal-insulator-metal) waveguide and a rectangular cavity is reported, which can support double Fano resonances originating from two different mechanisms. One of Fano resonance originates from the interference between a horizontal and a vertical resonance in the rectangular cavity. And the other is induced by the asymmetry of the plasmonic structure. Just because the double Fano resonances originate from two different mechanisms, each Fano resonance can be well tuned independently by changing the parameters of the rectangular cavity. And during the tuning process, the FOMs (figure of merit) of both the Fano resonances can keep unchanged almost with large values, both larger than 650. Such, the transmission spectra of the plasmonic structure can be well modulated to form transmission window with the position and the full width at half maximum (FWHM) can be tuned freely, which is useful for the applications in sensors, nonlinear and slow-light devices.