This paper present a study of carrier transport in graphene nanoribbon (GNR) transistors using three-dimensional quantum mechanical simulations based on a real-space approach of the non-equilibrium Greens function formalism in the ballistic and dissipative limit. The carrier transport parameters are determined in the presence of electron-phonon scattering, and its influence on carrier mobility including both optical phonons (OPs) and acoustic phonons (APs). The performances of GNR field effect transistors (GNRFETs) are investigated in detail considering the third nearest neighbour tight-binding approximation. The low-field mobility is extracted in the presence of AP and OP as a function of nanoribbon width and length, from which the diffusive/ballistic limit of operation in GNRFETs is determined. © 2012 American Institute of Physics.