A low complexity computational model of the current-voltage characteristics for graphene nanoribbon (GNR) field effect transistors (FET), being able to simulate a hundred points in a few seconds using a personal computer, is presented. For quantum capacitance controlled devices, self-consistent calculations of the electrostatic potential can be skipped. Instead, an analytical closed-form electrostatic potential from Laplace's equation yields accurate results compared with that obtained by the self-consistent non-equilibrium Green's functions (NEGF) method. The model includes both tunneling current through the Schottky barrier (SB) at the contact interfaces and thermionic current above the barrier, properly capturing the effect of arbitrary physical and electrical parameters. © IOP Publishing Ltd.