We compute the optical absorption, density of states and optical coefficients of graphene armchair nanoribbon under spin-orbit coupling effects. Kane–Mele model Hamiltonian has been applied for obtaining electronic band structure of graphene armchair nanoribbon in the presence of magnetic field and gap parameter. The effects of magnetic field and spin-orbit coupling strength on the frequency behavior of optical absorption of graphene armchair nanoribbon have been investigated. Also the frequency behavior of optical absorption of gapped graphene armchair nanoribbon has been studied due to magnetic field, spin-orbit coupling and gap parameter. Linear response theory and Green’s function approach have been exploited to obtain the frequency behavior of optical behavior of the structure. Moreover, the transmissivity and reflectivity of electromagnetic wave between two media separated by a graphene armchair nanoribbon are given. Our numerical results indicate that the frequency dependence of optical absorption includes a peak due to applying magnetic field. Also the frequency dependence of transmissivity and reflectivity of electromagnetic wave between two media separated by graphene armchair nanoribbon for normal incidence has been investigated due to effects of magnetic fields and spin-orbit coupling.