A novel membrane heat exchanger was proposed and analyzed. It was expected that the novel heat exchanger could be applied to the lithium bromide absorption chiller. Polyvinylidene fluoride hollow fiber module was adopted as the solution heat exchanger. The hot feed solution from the generator flowed into the lumen side of the membranes while the cold feed solution from the absorber flowed away from the shell side. Heat transfer and mass transfer occurred simultaneously in the membrane module, and only water vapor could diffuse across the membrane pore due to the water vapor pressure difference between the inside and outside of the membrane. Mathematical equations of the heat and mass transfer processes in the membrane heat exchanger were built, and the parallel flow process and the counter flow process were compared by numerical simulation. The simulation results show that the counter flow process was the better flow mode because the mean temperature difference was larger and the mass transfer was more steadily from the lumen side to the shell side. The heat caused by water vapor mass transfer may account for one-third of the total heat transfer. As a result, the membrane heat exchanger not only reinforced the heat recovery but also enlarged the deflation range and reduced the circulation rate and the heat loads of the generator and absorber. Eventually, the coefficient of performance of the heat exchanger was increased.