The liquid desiccant air-conditioning system is considered as an energy-efficient alternative to the vapor compression system. The dynamic response characteristics of the system under variable cooling load play an important role in the air temperature and humidity control performance of the system. However, the dynamic response characteristics have not been fully revealed in previous studies. Thus, a dynamic model for a heat pump driven liquid desiccant air-conditioning (HPLDAC) system is established to investigate the dynamic response characteristics of the system in this study. Subsequently, experiments were conducted to validate the accuracy of the dynamic model. The simulation results show a good agreement with the experimental data. The simulation results reveal that evaporating water from the solution is a time-consuming process, compared to adding water to the solution. It spends a long time for the HPLDAC system to decrease the high relative humidity of supply air to a low value, which limits the air temperature and humidity control performance of the system. The upper band for the water replenishing value opening (Δφup) is a crucial parameter to improve the limitation. When Δφup decreases from 1.0% to 0.25%, the time consumed to reduce the supply air relative humidity to the new lower set value can be saved by 30.6%.