In proton-exchange membrane fuel cells, it is particularly important to maintain appropriate water content and temperature in the electrolyte membrane. Taking into account the diffusion of water, the pressure variation, and the electro-osmotic drag in the membrane and using an empirical relationship between electro-osmotic drag and water content, a transport equation for membrane water molar concentration was obtained, and a new equation for the electric potential that strictly accounts for variable water contents was derived. The new potential equation is more accurate than the conventionally employed Laplace's equation. A number of numerical simulations are performed for comparing the new model with other results obtained computationally or experimentally. The relationship between the humidity in fuel cell and the electric potential loss within the membrane is also investigated at different nominal current densities. The impact and importance of three-dimensionality, relative humidity, temperature, and pressure non-uniformity are assessed and discussed.