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We report the tunable enhanced transmission of light through a hybrid metal–graphene structure, in which a graphene ribbon array is situated over a metallic grating. The graphene ribbon is employed to make the graphene–insulator–metal waveguide of finite length as a Fabry–Perot (F–P) cavity. When the slit of metallic grating is opened at the position with a maximal magnetic field in F–P resonant cavity, the transmission of light through metallic grating is greatly enhanced since the strongly localized magnetic field is effectively coupled to the slit. The transmission spectrum and the enhancement factor can be adjusted by changing geometrical parameters including the width and the length of slit, the width of graphene ribbon and the period of metallic grating. The transmission peaks exhibit a broad tuning range with a small change in the Fermi energy level of graphene. Moreover, the enhancement factor of transmission peak can be manipulated by the Fermi energy level and the carrier mobility of graphene, and an enhancement factor of 154 is obtained. The findings expand our understanding of hybrid metal–graphene plasmons and have potential applications in building active plasmonic devices. [ABSTRACT FROM AUTHOR]