Tunable plasmon-induced transparency (PIT) is realized for the mid-infrared region only by using two parallel graphene sheets over silicon diffractive gratings. The guided-wave resonances (GWRs) of the combined structure create a sharp notch on the normal-incidence transmission spectrum behaving as the bright resonators. The weak hybridization between the two bright modes results in the novel PIT optical response. The performance of the PIT system can be controlled by variation of geometrical parameters of silicon grating. Also, the resonance frequency of transparency window can be dynamically tuned by varying the Fermi energy of the graphene sheets via electrostatic gating instead of refabricating the structures. This study can be used for design of the optical ultra-compact devices and photonic integrated circuits