The invention relates to an air source heat pump clothes dryer with an adsorption and energy storage device. A refrigerant circulating loop for refrigerant to circulate and flow is composed of a compressor, a refrigerant channel of a condenser, a throttling device and a refrigerant channel of an evaporator, and an air circulating loop for air to circulate and flow is composed of an air channel of the condenser, a main draught fan, a clothes drying tub and an air channel of the evaporator. One end of the adsorption and energy storage device is communicated with an air pipe between the clothes drying tub and the evaporator, and the other end of the adsorption and energy storage device is communicated with an air pipe between the evaporator and the condenser. A first three-way valve is arranged on an air pipe between the main draught fan and the clothes drying tub. A second three-way valve is arranged on an air pipe between the adsorption and energy storage device and the condenser. The first three-way valve and the second three-way valve are communicated through an air pipe. A first air valve is arranged between the adsorption and energy storage device and the evaporator. Compared with the prior art, the clothes dryer has the advantages that by introducing the adsorption and energy storage device to the heat pump clothes dryer, the electric energy utilization efficiency of the clothes dryer is further improved, and meanwhile the clothes drying time is shortened.