We develop a numerical model for the current-voltage characteristics of organic electrochemical transistors (OECTs) based on steady-state Poisson’s, Nernst’s and Nernst–Planck’s equations. The model starts with the doping–dedoping process depicted as a moving front, when the process at the electrolyte–polymer interface and gradually moves across the film. When the polymer reaches its final state, the electrical potential and charge density profiles largely depend on the way the cations behave during the process. One case is when cations are trapped at the polymer site where dedoping occurs. In this case, the moving front stops at a point that depends on the applied voltage; the higher the voltage, the closer the stopping point to the source electrode. Alternatively, when the cations are assumed to move freely in the polymer, the moving front eventually reaches the source electrode in all cases. In this second case, cations tend to accumulate near the source electrode, and most of the polymer is uniformly doped. The variation of the conductivity of the polymer film is then calculated by integrating the density of holes all over the film. Output and transfer curves of the OECT are obtained by integrating the gate voltage-dependent conductivity from source to drain.