The equilibrium moisture contents of mango sheets were determined at 40–60°C and 11%–82% relative humidity (RH). The effects of RH and temperature of the drying air were investigated. The main objectives were: (a) to determine the moisture sorption isotherms and (b) to investigate the effects of applying hot air combined with RH control on mango sheet drying to imitate heat pump drying. Peleg's model was the best‐fitting model for the equilibrium moisture content. Controlling the RH at 15% clearly raised the drying rate after drying for 2 hr compared to drying without any RH control. Single‐stage drying at 60°C and 15% RH and two‐stage drying both required shorter drying times and provided superior mango color and textural qualities than the single‐stage drying at 60°C without any RH control. These results implicitly indicated the potential of heat pump dryer in the mango sheet drying. Novelty impact statement The moisture sorption isotherms together with the equations developed in this study are beneficial for the operation of heat pump dryer in mango sheet drying. The hot air combined with relative humidity control was applied in mango sheet drying experiments in order to imitate the drying air conditions occurring in a heat pump dryer. This study revealed that the application of heat pump dryer in the commercial drying of mango sheet or other agricultural products is interesting because this drying technique has potential to obtain the uniformity of moisture content of products without the necessity of opening the drying chamber to switch the positions of either trays or trolleys inside the drying chamber along the whole drying process which is both time‐ and labor‐consuming and increases the risk of contamination.