In this work a double-deck structure consisting of graphene nanoribbons is proposed, and the plasmonic properties of the system is investigated at mid-infrared wavelengths. In the structure, two graphene nanoribbon arrays with different parameters are coated on both sides of a glass substrate. With respectively varying the Fermi energies, the layer numbers of the graphenes, and the widths of the ribbons, the light transmittance is studied in the wavelength region from 5 to 30μm, via the finite difference time domain method. Multiple plasmonic resonances are revealed in the double-deck graphenes. It is shown that the plasmonic resonance properties including the resonance wavelengths, the peak intensities, and the peak widths can be adjusted by changing the parameters of the graphenes. The results suggest that the double-deck graphene nanoribbon structure proposed in this work be implemented in designs of plasmonic devices in mid-infrared regime.