In this work we develop a computational, quantum level monolayer graphene nanoribbon (GNR) MOSFET of channel length of 10 and 20 nm, with a width of 2 nm and contacts of 2nm width is attached. To develop the MOSFET channel, a bottom up approach is adopted by developing the material model. First the material models of graphene nanoribbon is developed using pybinding module tool in python. The material models of monolayer, bilayer graphene nanoribbon are built on the principles of tight binding module. The methodology developed is based on the Hamiltonian matrix formulation that has been used to determine the E-k plots and LDOS plots of graphene monolayer, bilayer graphene nano ribbon. The GNR MOSFET that is structurally built in python is used to simulate graphene as a switch. Its band gap characteristics is presented as its performance as a switch and is verified with relevant work. Then GNR MOSFET is modelled using quantum principles of NEGF and greens function to determine the transmission characteristics and the I-V characteristics for channel lengths of 10 nm and 20 nm.