Graphene can be utilized in designing tunable terahertz (THz) devices due to its tunability of sheet conductivity, suffering however with weak light-graphene interactions. In this paper, an absorption enhancement in graphene using a Fabry–Perot resonator is presented, and its performance has been numerically investigated using finite element method. The Fabry–Perot resonator consists of a continuous layer of graphene film sandwiched between the polymethyl methacrylate and silicon layers on an Au substrate which is covered by periodic gold ribbons. Numerical results show that the absorption performance is significantly enhanced by use of the Fabry–Perot resonator and a narrow band perfect absorption is achieved in THz regime. The influence of structural parameters on the absorption performance is further analyzed, and the absorption peak frequency can be flexibly controlled by adjusting the chemical potential of graphene which could be conveniently achieved by applying a bias voltage. The proposed structure here has a promising potential for developing advanced THz optics-electronics devices.