With exhausting fossil fuels and increasing demand for heating and cooling, the effective utilization of renewable and waste energy sources becomes of increasing importance. Adsorption cooling driven by low temperature heat is an energy and environment saving alternative to the common compression systems. The performance of adsorption chillers strongly depends on the compliance of the adsorbent properties with the cycle operating conditions. In this paper, the comprehensive study of equilibrium and dynamics of water adsorption on a new efficient adsorbent of water vapour MOF-801 is performed to evaluate its feasibility for adsorption cooling. It was shown that at the adsorption temperature of 30 °C the MOF-801 provides the cooling effect at the evaporation temperature as low as 5 °C that indicates significant affinity to water vapour. On the other hand, it can be regenerated by low temperature heat at 80–85 °C. The uptake variation under the conditions of a typical adsorption cooling cycle reaches 0.21 g/g. Water adsorption on loose grains of MOF-801 occurs under grain-size insensitive mode when the adsorption rate is proportional to the (S/m)-ratio of the heat transfer surface S to the adsorbent mass m. The Specific Cooling Power equal to 2 kW/kg is measured at S/m = 6 m2/kg and 80% of reaching the equilibrium conversion, which is of high practical interest. Thus, the results obtained demonstrate the high potential of the working pair “MOF-801 – water” for adsorption cooling.