The invention discloses an air source heat pump water heater with a double-water tank system. The water heater comprises a main machine, a heating water tank, a heat-preservation water tank and a controller, wherein the heating water tank is parallelly connected with a water supplementing system consisting of a water meter, a first electromagnetic valve, a first ball valve and a first check valve; the heat-preservation water tank is connected with a water supply system consisting of a fourth electromagnetic valve, a second ball valve and a third ball valve; and the main machine forms a hot water circulating system together with a second electromagnetic valve, a third electromagnetic valve, the fourth electromagnetic valve, a fifth electromagnetic valve and a second check valve. The heating water tank, a first high water level switch, a first low water level switch, a heating water tank temperature sensor, the heat-preservation water tank, a second high water level switch, a second low water level switch and a heat-preservation water tank sensor form a water storage system. A fourth ball valve, a fifth ball valve, a first butterfly valve, a second butterfly valve, a second circulating water pump and a target flow switch form a cleaning system. The water heater can reduce working temperature spots and power consumption of a machine set and improve the COP value of the machine set effectively.