Single and bilayer graphenes have received considerable attention since the fabrication of Graphene nanoribbon (GNR) by Wang et al.  due to its excellent transport properties. Bilayer GNR consists of two weakly, van der Waals stacked honeycomb sheets of carbon atoms in a Bernal stacking [2,3] as can be seen in figure 1. The stacking layers are separated for about 0.3 nm . The band structure of single layer graphene has linear dispersion relation whilst bilayer graphene has a quadratic dispersion  which provides an interesting venue research activity. In addition, these materials also offer useful electronics application because of its high carrier mobility which is crucial for the field-effect transistor operation. The carrier mobility in turn related to the conductance governed by the conductivity theory in which it helps indicate the transport performance of the bilayer GNR especially for the use of GNR as a conducting channel, connecting the source and drain electrodes.