Moisture management in proton exchange membrane fuel cells is crucial to durability and performance. This frequently requires external humidification of the reactant gas streams to maintain sufficient humidity levels at the membranes, especially at higher operating temperatures. Direct-contact humidifiers using louvered fins brazed to rectangular tubes, similar to those frequently employed in automotive condensers and radiators, can be used to humidify a gas stream. A gas stream in which liquid water is sprayed flows through the passages formed by the louvered fins counter-current to a heating fluid flowing in the rectangular tubes sandwiching the fins. A mathematical model of this type of direct-contact humidifier is presented. The equations of energy and mass conservation are simultaneously solved for a number of segments along the humidifier. An equivalent resistance network is used to capture the temperature profile of the fins and liquid film surrounding them. The thickness of the liquid film is calculated from a shear balance at the film interface. The heat and mass transfer analogy is used with empirically derived transfer coefficients to solve the coupled heat and mass transfer problem in the gas phase. Predicted results are presented for typical operating conditions corresponding to a wide range of fuel cell operating conditions. The results show how the humidification process varies along the length of the humidifier. It is also shown that, although evaporation of the liquid film takes place throughout the entire humidifier, the direction of sensible heat transfer between the gas and liquid film can switch at some distance along the humidifier. This confirms the need for the equivalent resistance network model of the fin and film since simple fin efficiency models would fail in this situation. The model provides a basis for design optimization and performance predictions for this type of direct-contact moisture management device.