In this paper, the magnetically tunable Goos–Hänchen (GH) shift of a reflected beam at terahertz frequencies is achieved by using a multilayer structure where three layers of anisotropic graphene are inserted. The enhanced GH shift phenomenon results from the local field enhancement owing to the excitation of graphene surface plasmon polaritons at the interface between two dielectric materials. By considering the quantum response of graphene, the GH shift can be switched from negative to positive by harnessing the anisotropic conductivity of graphene, and the GH shift can be actively tuned through the external magnetic field or by controlling the structural parameters. By setting appropriate magnetic field and structural parameters, we can obtain GH values of −140 microns to 220 microns in the terahertz band. This enhanced and tunable GH shift is promising for fabricating graphene-based terahertz shift devices and other applications in nanophotonics.