In this study, we construct a periodic array of a single layer graphene ribbon based on the surface electric current boundary condition. Further, the periodic array of graphene ribbon is investigated using a finite-difference time-domain simulation and the coupled-mode theory. The results show that the graphene array exhibits a typical surface plasma double-resonance effect in the mid-infrared band. Its periodic array structure can enhance the resonance effect of graphene surface plasma local field. The resonant wavelengths, electrical field energy, attenuation rate, and lifetime of the resonance mode of graphene surface plasma are analyzed. The simulation results demonstrate that the resonance wavelength can be tuned from 16.81 to 11.13 μm when the graphene Fermi energy is increased from 0.4 to 0.8 eV and that the plasma lifetime can be regulated from 21 to 223 fs when the graphene carrier mobility is increased from 0.1 to 1.0 m ²·(V·s) ^-1. Furthermore, the quality factor increases nonlinearly from 0.14 to 0.19 when the refractive index of the superstrate is increased from 1 to 2. The research methods and conclusions of this study are useful for designing graphene plasma devices.