A polymer electrolyte membrane (PEM) fuel cell is probably the most promising technology that will replace conventional internal combustion engines in the near future. As a primary power source for an automobile, the transient performance of a PEM fuel cell is of prime importance. In this thesis, a comprehensive, three-dimensional, two-phase, multi-species computational fuel cell dynamics model is developed in order to investigate the effect of flow-field design on the magnitude of current overshoot/undershoot and characteristics of current response when the cell is subjected to different voltage change patterns representing an automotive operation. The meshing strategy specific to PEM fuel cell modelling is studied in a systematic manner and employed in all analyses presented in this thesis. The predicted results compare very well with experimental data under both steady-state and transient operations. Two computational domains are used – the straight single-channel and practical-scale square cells with parallel, single-serpentine, and triple-serpentine flow-fields. The results from the straight single-channel cell suggest that the magnitude of current overshoot/undershoot increases with the voltage change rate. The behaviour of a current response curve is the result of complex interplay between water content at both sides of the membrane. It is also found that current overshoot/undershoot is amplified with the presence water flooding in the cell. The results from the square cell reveal that current overshoot/undershoot is caused by non-uniformity of local current density over the active area confirming the effect of flow-field geometry on transient response of the cell. By comparing the transient performance between the three flow-fields, a direct relationship between degree of water flooding in the cell and magnitude of current overshoot/undershoot has been found. A conclusion has been drawn which states that a cell with superior water removal ability will experience smaller current overshoot/undershoot.