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A monolayer-graphene-based concentric-double-rings (CDR) structure is reported to achieve broadband plasmon-induced transparency (PIT) on the strength of edge mode in the mid-infrared regime. The theoretical analysis and simulation results reveal that the structure designed here has two plasmonic resonance peaks at 39.1 and 55.4 THz, and a transparency window with high transmission amplitude at the frequency of 44.1 THz. Based on the edge mode coupling between neighbor graphene ribbons, PIT phenomenon is produced through the interference between different (bright and dark) modes. The frequency and bandwidth of the transparency window and slow light time could be effectively adjusted and controlled via changing geometrical parameters of graphene or applying different gate voltages. Additionally, this structure is insensitive to the polarization and incident angle. This work has potential application on the optical switches and slow light modulators.