We present an atomistic three-dimensional simulation of graphene nanoribbon field effect transistors (GNR-FETs), based on the self-consistent solution of the 3D Poisson and Schroedinger equation with open boundary conditions within the non-equilibrium Greens Function formalism and a tight-binding hamiltonian. With respect to carbon nanotube FETs, GNR-FETs exhibit comparable performance, reduced sensitivity on the variability of channel chirality, and similar leakage problems due to band-to-band tunneling. Acceptable transistor performance requires effective nanoribbon width of 1-2 nm, that could be obtained with periodic etching patterns or stress patterns.