We analytically investigate distributed circuit modeling of the tunable-enhanced Goos-Hänchen shift of light beams from a Graphene containing structure which supports TM surface waves. Here the coupling of the incident wave to the surface modes of the structure is used to enhance the Goos-Hänchen shift of the totally reflected wave. It is also shown that this large lateral shift can be controlled trough controlling the dispersion properties of the surface modes by applying an electrical voltage to the Graphene layer. A distributed circuit model is proposed for the Graphene containing structure and used to calculate the reflection coefficient of the structure. Phase of the reflection coefficient is then used to calculate the Goos-Hänchen shift. Our calculations show that by coupling the incident wave to the surface modes of the structure large Goos-Hänchen shift as high as 100 times of the free space wavelength can be achieved. Furthermore this large shift can be tuned by apply relatively small voltages in order of 8 volts to the structure. Therefore, the proposed structure can be used for adjustable broadband switches.