In this study, we design a plasma refractive index sensor with a cross tie-shaped graphene array structure. Further, the double-resonance transmission phenomenon in the mid-infrared band can be obtained by using the surface plasmon effect produced by the interface between the graphene and dielectric, and the dynamic regulation of the transmission spectrum can be realized by combining the electrically adjustable characteristics of graphenes. Subsequently, the effects of the chemical potential, number of layers, and geometric parameters of graphenes on the double-resonance transmission phenomenon in the structure are studied using the finite-difference time-domain method. The results denote that the resonance position can be tuned by changing the chemical potential and the number of layers of the graphene. Compared with a traditional sensor, this structure exhibits better sensing performance and double-resonance transmission phenomenon after the structural parameter optimization. The sensitivities of two resonance valleys are as high as (1280±24) and (2800±49) nm/RIU with quality factors of 17.1 and 12.3 RIU -1, respectively. These results provide a theoretical basis for the graphene plasma biosensor design.