We report on a new computational model to efficiently simulate carbon nanotube-based field effect transistors (CNT-FET). In the model, a central region is formed by a semiconducting nanotube that acts as the conducting channel, surrounded by a thin oxide layer and a metal gate electrode. At both ends of the semiconducting channel, two semi-infinite metallic reservoirs act as source and drain contacts. The current-voltage characteristics are computed using the Landauer formalism, including the effect of the Schottky barrier physics. The main operational regimes of the CNT-FET are described, including thermionic and tunnel current components, capturing ambipolar conduction, multichannel ballistic transport and electrostatics dominated by the nanotube capacitance. The calculations are successfully compared to results given by more sophisticated methods based on non-equilibrium Green's function formalism (NEGF). © IOP Publishing Ltd.