A tunable Fano resonance based on a microring resonator is proposed. The double microring is nested in parallel in the U-shaped feedback waveguide with the graphene embedded in part of the waveguide as the active modulation region of Fano resonance. When different voltages are applied to the graphene in the feedback waveguide or microrings, the Fano resonance exhibits different and asymmetrical shapes and has a larger extinction ratio than the traditional Lorentz shape. The maximum extinction ratio of the proposed device is up to 71.50 dB. The proposed structure will have a wide application in sensors, switches, and integrated optoelectronic devices.