Composites combining salt hydrates and porous matrix like metal–organic frameworks (MOFs) are used to enhance the performance of thermochemical storage materials. However, the mechanism for the enhancement and the strategy for the selection of salt hydrates and porous matrix are not clear. The heat storage performance is determined by water adsorption dynamics, capacity and their sorption energy of the single components. The single components (salts or matrix) normally have either fast water adsorption dynamics or high-water uptake capacity, but not both of them. In this study, we investigate the enhancement of adsorption in composite materials, and a novel strategy is then proposed to combine the advantages from adsorbents with higher adsorption dynamics at low water partial pressure with those with a high capacity at high water partial pressure to promote the water adsorption capacity and kinetics, hence efficient energy storage. Two types of composites have been used to demonstrate the two-stage strategy developed in this study, in which SrCl2 and SrBr2 are incorporated into MOF MIL-101(Cr) to enhance adsorption and heat storage. In these composites, SrCl2 and SrBr2 can be regarded as the moisture pumps, capturing water vapour from air to improve the adsorption dynamics, while MIL-101(Cr) with high adsorption capacity functions as a water reservoir to take the water accumulated by the salts. Through this two-stage design, the water sorption capacity of the composites is 2–3 times higher than the water uptake of either salts or MOF within 120 min. As SrCl2 has a faster water adsorption kinetics than SrBr2, SrCl2/MIL-101(Cr) reaches an uptake of 0.73 g/g, however, the water sorption capacity of SrBr2/MIL-101(Cr) is 0.54 g/g. The composite samples also present good heat storage capacities of 1462 J/g for SrCl2/MIL-101(Cr) and 1526 J/g for SrBr2/MIL-101(Cr), and good cycling stability after 15 repeating adsorption/desorption cycles.