A laboratory-scale liquid-feed direct methanol fuel cell (DMFC) was operated with different methanol feeding strategies. A proton exchange membrane (PEM) was used as the elecytrolyte. The cell voltage response to dynamic feeding of methanol revealed that a significant voltage increase can be obtained from dynamic changes in methanol feed concentration. The observed fuel cell behaviour was analysed with a mathematical model which consists of anode mass balances, charge balances of both electrodes and electrode kinetic expressions. Anode kinetics were derived from a four-step reaction mechanism with several intermediates bound to the catalyst surface. The model also accounts for the undesired cross-over of methanol, through the PEM, towards the cathode catalyst layer. First, the model is applied to predict steady-state current-voltage characteristics. Then, the cell voltage response to dynamic changes of methanol feed concentration is simulated. The simulated results are in full agreement to experimental observations. It turns out that methanol cross-over can be reduced by periodically pulsed methanol feeding.