We present a controlled Fano resonance in the mid-infrared (MIR) region from a kind of plasmonic metasurface consisting of a single-atom-thick surface layer with a periodic pattern of graphene nanostrip pairs on a dielectric substrate. Both the numerical and theoretical results indicate that the Fano resonance spectrum can be flexibly tailored through adjusting the geometrical parameters, such as the asymmetric distance and coupling gap between each pair of graphene nanostrips. Particularly, we achieve the dynamic tunability of the plasmonic Fano resonance spectrum by controlling the polarization of incident light and the Fermi level of graphene. The theoretical calculations agree well with the numerical simulations. These results could find significant applications in nanoscale light control and functional devices operating in the MIR region. (C) 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement.