This paper presents a simplified zero-dimensional mathematical model for a self-humidifying proton exchange membrane (PEM) fuel cell stack of 1 kW. The model incorporates major electric and thermodynamic variables and parameters involved in the operation of the PEM fuel cell under different operational conditions. Influence of each of these parameters and variables upon the operation and the performance of the PEM fuel cell are investigated. The mathematical equations are modeled by using Matlab–Simulink tools in order to simulate the operation of the developed model with a commercial available 1 kW horizon PEM fuel cell stack (H-1000), which is used for the purposes of model validation and tuning of the developed model. The model can be extrapolated to higher wattage fuel cells of similar arrangements. New equation is presented to determine the impact of using air to supply the PEM fuel cell instead of pure oxygen upon the concentration losses and the output voltage when useful current is drawn from it.