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Abstract A graphene-based on-chip plasmonic nanostructure composed of a plasmonic bus waveguide side-coupled with a U-shaped and a rectangular nanocavities has been proposed and modeled by using the finite element method in this paper. The dynamic tunability of the plasmon-induced transparency (PIT) windows has been investigated. The results reveal that the PIT effects can be tuned via modifying the chemical potential of the nanocavities and plasmonic bus waveguide or by varying the geometrical parameters including the location and width of the rectangular nanocavity. Further, the proposed plasmonic nanostructure can be used as a plasmonic refractive index sensor with a sensing sensibility of 333.3 nm/refractive index unit (RIU) at the the PIT transmission peak. Slow light effect is also realized in the PIT system. The proposed nanostructure may pave a new way towards the realization of graphene-based on-chip integrated nanophotonic devices.