In this paper, a mathematical model is developed to study the performance of a polymer membrane electrolyser (PEM) and the effect of different parameters including operating temperature, cathode pressure, membrane thickness, the width and height of channel and current density on the performance and energy and exergy efficiency of PEM electrolyser are investigated. In addition to the resistance overvoltage of components, the concentration overvoltage is modeled using an accurate equation. The model is validated against experimental data. The results indicate that by increasing current density, the voltage of the electrolyser increases, and energy and exergy efficiencies reduce. Increase of temperature from 313 K to 353 K, and decrease of cathode pressure from 40 bar to 1 bar lead to decrease of voltage of the PEM electrolyser by 8.3% and 4.8%, respectively. Moreover, energy and exergy efficiencies increase between 2% and 6% in the range of working temperature and pressure. It is concluded that decrease of membrane thickness, height and width of channel, and increase of exchange current density of the anode and cathode electrodes lead to decrease of voltage of the electrolyser and increase of energy and exergy efficiencies. However, the effect of temperature and cathode pressure and the exchange current densities is greater than the effect of geometric parameters. (C) 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.