The structure for implementing resonant optical tunneling effect (ROTE) is a simple layered system of dielectrics that provides full light transmission for resonance condition, despite the presence of barrier layers partially locking light. The presence of a sharp resonant peak both for the intensity and for the spatial shift of the transmitted light beam makes such a structure promising for the creation of sensors and light control devices. This paper focuses on the spatial shift called the Goos-Hänchen shift of such a structure with interfaces of the waveguide layer coated by graphene. The effect of Goos-Hänchen shift near the resonance in this case may be caused by small changes in the chemical potential or the Fermi energy of graphene, which can be controlled both chemically and by electrical bias. The characteristics of transmitted light beam strongly depend on the beam width for the selected optimal focusing condition.