Latent cooling load accounts for 30% of the total load of air-conditioning, and its proportion is even higher in many tropical and subtropical climates. Traditional vapour-compression air-conditioning (VCAC) has a low coefficient of performance (COP) due to the refrigeration dehumidification process, which often makes necessary a great deal of subsequent re-heating. Technologies using conventional desiccants or sorbents for indoor moisture control are even less competitive than VCAC due to their high regeneration temperature, long cycling time and bulky components. Here, we report a novel high temperature cooling system that uses porous metal-organic frameworks (MOFs) as advanced sorbents for humidity control. We directly coat MOFs on the surface of evaporator and condenser. The system has no additional components compared to a traditional VCAC. The evaporator can simultaneously remove both the sensible and latent loads of the incoming air without reducing the temperature below its dew point. The regeneration of wet MOFs is completely driven by the residual heat from the condenser. The MOF-coated heat exchangers can achieve a cooling power density of 82 W·L-1. We demonstrate that the system has a high COP, up to 7.9, and can save 36.1% of the energy required, compared to the traditional VCAC system with reheating. The amphiphilic MOFs used in the research have high water uptake, are made of low-cost raw materials and have high hydrothermal stability. They thus have the potential for being scaled up for large-scale applications in air conditioning.