With the help of the resonance effect of graphene nanoribbon arrays, a three-layer graphene nanoribbon array is proposed. The influences of the various parameters of this array on the multi-frequency filtering characteristics of the composite structure are investigated. With the finite-difference time-domain (FDTD) method, the influences of Fermi level, graphene bandwidth ratio, and external refractive index on filter frequency are discussed. The research results show that the increase of Fermi level can make the resonant frequency blue shift, in contrast, the increase of graphene bandwidth ratio and external refractive index can both make the resonant frequency red shift. When Fermi level is changed by 0.1 eV, the resonant frequency can be changed by an amount of more than 5 THz.