► Water desalinated in a humidification/dehumidification unit. ► Experiment and theoretical model agree for distillate production and temperature. ► Enthalpy of condensation recovered as sensible heat up to 85% . A desalination system based on the humidification and dehumidification of air is studied. The evaporator unit is based on a treated cellulose paper substratum through which water flows, and which has a large area to favor evaporation. The condenser unit is a liquid–gas heat exchanger, where water vapor is condensed and the enthalpy of condensation is recovered to preheat the water. The mathematical model and experimental results are presented and it is shown that they present a good agreement. Some operating conditions for better heat recovery are presented.