A mathematical model related to PEM electrolyzer combined thermodynamic principles and electrochemical equations is developed. The model was validated through a comparison of the polarization curves (J–V) predicted by the present approach with those reported by Ni et al. The simulation shows that there is good accuracy between the results. The study investigates how operating conditions such as temperature, ionic conductivity of the membrane, thickness, as well as energy and exergy efficiencies influence the electrolyzer’s behavior. The results reveal that the cell potential declines as the temperature rises. The cause of that is the drop of the ohmic overpotential, which is related to the membrane ionic conductivity. The results show that the ionic conductivity rises with temperature. Thus, a larger water content has a slight effect on the electrolyzer performance. Also, raising the membrane thickness causes an increase in the ohmic overpotential. To recapitulate, the findings highlight that using a thinner membrane reduces ohmic losses, which enhances the cell’s performance. Moreover, higher water content was found to improve both energy and exergy efficiencies.