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Abstract A suspended monolayer graphene has only about 2.3% absorption rate in visible and infrared band, which limits its optoelectronic applications. To significantly increase graphene’s absorption efficiency, a tunable dual-band and polarization-insensitive coherent perfect absorber (CPA) is proposed in the mid-infrared regime, which contains the silicon array coupled in double-layers graphene waveguide. Based on the FDTD methods, dual-band perfect absorption peaks are achieved in 9611 nm and 9924 nm, respectively. Moreover, due to its center symmetric feature, the proposed absorber also demonstrates polarization-insensitive. Meanwhile, the coherent absorption peaks can be all-optically modulated by altering the relative phase between two reverse incident lights. Furthermore, by manipulating the Fermi energies of two graphene layers, two coherent absorption peaks can move over a wide spectrum range, and our designed CPA can also be changed from dual-band CPA to narrowband CPA. Thus, our results can find some potential applications in the field of developing nanophotonic devices with excellent performance working at the mid-infrared regime.