The invention discloses a heat-pump water heater with dual water tanks and a heating method thereof. The heat-pump water heater with dual water tanks comprises a compressor, a condenser, a liquid storage device, a drying filter, a throttle device, an evaporator, a gas-liquid separator, a heat-storing water tank, a heating water tank, a reversing device and the like, wherein the reversing device periodically changes the flow direction of water in the heating water tank and the condenser, so that cold water in the heating water tank flows through the condenser to and fro and is gradually heated to a preset temperature; the heated hot water is transferred from the heating water tank to the heat-storing water tank and stored for users to use; cold water is simultaneously supplemented into the heating water tank in the transfer process and continuously heated to the preset temperature after the supplement is finished; and cold water is simultaneously supplemented into the hot water of the heat-storing tank during use. The insides of the heating water tank and the heat-storing water tank are in float rolling sleeve structures which are used for isolating the cold water from the hot water in the water tanks, thereby effectively reducing the irreversible heat loss inside the water tanks of an air source heat-pump water heater; in addition, the invention has the advantages of high efficiency, convenient installation and running, high safety, wide application range and the like.