A heat pump hot-water supply system, comprising: a heat pump water heater including a main circuit, in which a compressor configured to compress refrigerant, a gas cooler, a first solenoid valve (80V1), a regenerative heat exchanger, an expansion valve, and an air heat exchanger are connected in the stated order; a hot-water supply tank including a heat medium for exchanging heat with the refrigerant flowing through the gas cooler; and a heat storage tank including a heat medium for exchanging heat with the refrigerant flowing through the regenerative heat exchanger, the heat pump water heater including a first bypass formed to branch off the main circuit at a first branching portion located on an outlet side of the gas cooler and an inlet side of the first solenoid valve (80V1), and to merge with the main circuit at a first merging portion located on an outlet side of the regenerative heat exchanger and an inlet side of the expansion valve, a first bypass solenoid valve provided on the first bypass, and a control unit configured to switch the first solenoid valve (80V1) to be opened or closed, a second bypass formed to branch off the main circuit at a second branching portion located on a discharge side of the compressor and an inlet side of the gas cooler, and to merge with the main circuit (8,80) at a second merging portion located on the outlet side of the gas cooler and the gas cooler side of the first branching portion, a second bypass solenoid valve, provided on the second bypass, a second solenoid valve (80V2) provided on an outlet side of the expansion valve and an inlet side of the air heat exchanger; and a third bypass formed to branch off the main circuit on the outlet side of the expansion valve and an inlet side of the second solenoid valve (80V2), and to merge with the main circuit on an outlet side of the second solenoid valve (80V2) and the inlet side of the air heat exchanger, wherein the control unit operates a heat recovery and hot-water supply mode, and is configured to, in the heat recovery and hot-water supply mode, close the first solenoid valve (80V1), close the second solenoid valve (80V2), open the first bypass solenoid valve, and close the second bypass solenoid valve. a heat pump water heater including a main circuit, in which a compressor configured to compress refrigerant, a gas cooler, a first solenoid valve (80V1), a regenerative heat exchanger, an expansion valve, and an air heat exchanger are connected in the stated order; a hot-water supply tank including a heat medium for exchanging heat with the refrigerant flowing through the gas cooler; and a heat storage tank including a heat medium for exchanging heat with the refrigerant flowing through the regenerative heat exchanger, the heat pump water heater including a first bypass formed to branch off the main circuit at a first branching portion located on an outlet side of the gas cooler and an inlet side of the first solenoid valve (80V1), and to merge with the main circuit at a first merging portion located on an outlet side of the regenerative heat exchanger and an inlet side of the expansion valve, a first bypass solenoid valve provided on the first bypass, and a control unit configured to switch the first solenoid valve (80V1) to be opened or closed, a first bypass formed to branch off the main circuit at a first branching portion located on an outlet side of the gas cooler and an inlet side of the first solenoid valve (80V1), and to merge with the main circuit at a first merging portion located on an outlet side of the regenerative heat exchanger and an inlet side of the expansion valve, a first bypass solenoid valve provided on the first bypass, and a control unit configured to switch the first solenoid valve (80V1) to be opened or closed, a second bypass formed to branch off the main circuit at a second branching portion located on a discharge side of the compressor and an inlet side of the gas cooler, and to merge with the main circuit (8,80) at a second merging portion located on the outlet side of the gas cooler and the gas cooler side of the first branching portion, a second bypass solenoid valve, provided on the second bypass, a second solenoid valve (80V2) provided on an outlet side of the expansion valve and an inlet side of the air heat exchanger; and a third bypass formed to branch off the main circuit on the outlet side of the expansion valve and an inlet side of the second solenoid valve (80V2), and to merge with the main circuit on an outlet side of the second solenoid valve (80V2) and the inlet side of the air heat exchanger, wherein the control unit operates a heat recovery and hot-water supply mode, and is configured to, in the heat recovery and hot-water supply mode, close the first solenoid valve (80V1), close the second solenoid valve (80V2), open the first bypass solenoid valve, and close the second bypass solenoid valve.