In this Letter, we have shown that a giant Goos–H nchen shift of a light beam reflected at terahertz frequencies can be achieved by using a composite structure, where monolayer graphene is coated on one-dimensional photonic crystals separated by a dielectric slab. This giant Goos–H nchen shift originates from the enhancement of the electrical field, owing to the excitation of optical Tamm states at the interface between the graphene and one-dimensional photonic crystal. It is shown that the Goos–H nchen shift in this structure can be significantly enlarged negatively and can be switched from negative to positive due to the tunability of graphene’s conductivity. Moreover, the Goos–H nchen shift of the proposed structure is sensitive to the relaxation time of graphene and the thickness of the top layer, making this structure a good candidate for a dynamic tunable optical shift device in the terahertz regime.