The impact of spontaneously generated coherence (SGC) on the Goos-Hänchen (GH) shifts of transmitted and reflected light beams from a cavity with a four-level rubidium atom with a Rydberg state are discussed. Using the quantum mechanical density matrix method, we first discuss the absorption and dispersion properties of the medium, then analyze the GH shifts of transmitted and reflected light beams, respectively. We find that quantum interference from SGC can modify the absorption-dispersion properties, which leads to enhancement in GH shifts in transmitted and reflected light beams. Moreover, the effects of coupling light and its detuning on the properties of GH shifts have been discussed.