Polymer electrolyte membrane direct methanol fuel cells (PEM-DMFCs) have several advantages over hydrogen-fuelled PEM fuel cells; but sluggish methanol electrochemical oxidation and methanol crossover from the anode to the cathode through the PEM are two major problems with these cells. In the present work, a comprehensive one-dimensional, single phase, isothermal mathematical model is developed for a liquid-feed PEM-DMFC, taking into account all the necessary mass transport and electrochemical phenomena. Diffusion and convective effects are considered for methanol transport on the anode side and in the PEM, whereas only diffusional transport of species is considered on the cathode side. A multi-step reaction mechanism is used to describe the electrochemical oxidation of methanol at the anode. Stefan-Maxwell equations are used to describe multi-component diffusion on the cathode side and Tafel type of kinetics is used to describe the simultaneous methanol oxidation and oxygen reduction reactions at the cathode. The model fully accounts for the mixed potential effect caused by methanol crossover at the cathode. It shows excellent agreement with literature data of the limiting current density for different low methanol feed concentrations at different operating temperatures. At high methanol feed concentrations, oxygen depletion on the cathode side, due to excessive methanol crossover, results in mass-transport limitations. The model can be used to optimize the geometric and physical parameters with a view to extracting the highest current density while still keeping a tolerably low methanol crossover. © 2008 Elsevier B.V. All rights reserved.