A simulation method has been formulated to study the characteristics of a Graphene Field Effect Transistor (GFET). The method takes care of the effect of source and drain contact resistances while iteratively solving for the drain current. The results when compared with experimental data validate our modeling and simulation approach. The method has been used to investigate the effect of different gate dielectric materials and their dimensions on the output as well as transfer characteristics of the GFET. Our results open new ways for the possibility of dielectric engineered GFET characteristics suiting to the requirement of a given device application. The convergence of the point of inflexion for dual positive gated GFETs is interesting. The existence of a critical thickness for each dielectric material, beyond which the current saturates and the rise in its value with dielectric constant(εr), are some novel features worth attention.