This work reports on the plasmonic properties of composite arrays consisting of graphene nanoribbons and perovskite nanowires, in the mid infrared region of 5 -60 µm. In the array, a set of graphene nanoribbons are placed on the perovskite nanowires, which are embedded in a glass substrate. Two scenarios are investigated in this work; one is that the graphene and the perovskite are matched, while the other is that the graphene and the perovskite are mismatched. The light transmittance of the arrays is numerically simulated, via the finite difference time domain method. Multiple plasmonic resonances are observed, and the corresponding electric field distributions are calculated. The results demonstrate that the plasmonic characteristics of the arrays can be adjusted by varying the parameters including the chemical potential and the layer number of graphene, as well as the refractive index of perovskite, etc. In addition, a Fano lineshape is revealed in one of the resonance peaks of the transmittance. It is well fitted to the Beutler-Fano formula, and the characteristic q factor is determined. The results in this work may be useful in studies of similar plasmonic nanostructures that employ graphene and perovskite-based composite nanoarrays.