Graphene, composed of sp2 hybrid orbitals, is a hexagonal nanomaterial with a two-dimensional honeycomb lattice structure. Nowadays, thanks to its great electronic, optical, and thermal properties, there have been many promising applications based on graphene nanostructures. Under irradiations of external electromagnetic fields, the free electrons on graphene surfaces can be excited to oscillate collectively, resulting in highly localized surface plasmons. This phenomenon may provide foundations for designs of tunable plasmonic devices, therefore, graphene-based nanostructures have been widely studied so far. Besides, investigations on noble metals is another hot topic in the plasmonic community. With irradiations of incident lights, collective oscillations of free electrons on noble metals’ surfaces can also be induced, forming surface plasmons. The plasmonic characteristics can be adjusted by varying the parameters of the metals, including the geometries, thicknesses, as well as dimensions, etc. In this paper, a composite array consisting of graphene nanoribbons and noble metals is proposed, and its plasmonic properties are studied at mid-infrared wavelengths. In the structure, graphene nanoribbons are placed in between two SiO2 layers, and gold semi-cylinders and silver nanofilms are placed above the upper SiO2 layer, respectively. Using the finite difference time domain method, the light transmittance and electric field of the array are investigated, by varying the graphene’s Fermi energy and layer number, the noble metals’ sizes, as well as the period of the array, respectively. The results show that a plasmonic resonance feature is revealed in the 4–18 μm wavelength range, and the resonance characteristics can be tuned by adjusting the above parameters. The composite array structure proposed in this work may provide us with a new platform for the design of plasmonic devices in the mid-infrared regime.