[en] In this paper, we investigated coupling of confined photons in the semiconductor microcavity consists of Distributed Bragg Reflectors (DBR) (Si_3N_4/SiO_2 and AlAs/Al_0_._1Ga_0_._9As) with excitons of gapped Armchair Graphene NanoRibbon (A-GNR) that placed at the maximum of electric field amplitude inside the semiconductor microcavity. Our calculations show that the coupling between GNR's exciton and confined photon modes and appearance of vacuum Rabi splitting (VRS), is possible. By the means of Transfer Matrix Method (TMM) we obtain angle dependent reflectance spectrum and Upper, Lower Polariton Branches (UPB&LPB) for the structure. Clear anticrossing between the neutral exciton and the cavity modes with a splitting of about 3 meV obtained that can be enhanced in double-GNR. While, our calculations certify the formation of graphene based exciton-polariton, propose the enhancement of VRS by optimization of relevant parameters to implement the graphene based cavity polaritons in optoelectronic devices.