The mobility of electron denotes how quickly electron can move through any metal or semiconductor, when pulled by an electric field. In our work, we present an analytical device model specially for a Graphene Nanoribbon Field Effect Transistor (GNRFET). A highly conducting substrate whose mobility is very high plays a vital role of the back gate, but the top gate tends to control the drain current. In our model, we calculated the potential distributions in the GNRFET as a function of back gate voltage, top gate voltage and drain voltage.