A method for controlling a heat pump hot-water supply device including a first refrigerant cycle in which a first refrigerant circulates, and including a first compressor, an outdoor heat exchanger, and a first expansion device; a second refrigerant cycle, in which a second refrigerant circulates, and including a second compressor and a second expansion device; a water-refrigerant heat exchanger, to which the first refrigerant compressed in the first compressor and the second refrigerant compressed in the second compressor is introduced; a water introduction path coupled to a first side of the water-refrigerant heat exchanger and into which supplied water is introduced; and a water discharge path coupled to a second side of the water-refrigerant heat exchanger and from which the water heat-exchanged in the water-refrigerant heat exchanger is discharged; the method comprising: turning on the heat pump hot-water supply device and inputting a predetermined discharge water temperature; determining whether an outdoor air temperature is greater than a predetermined temperature; when the outdoor air temperature is greater than the predetermined temperature, driving only the first compressor, and when the outdoor air temperature is less than the predetermined temperature, driving the first and second compressors; and determining additional driving of the second compressor on the basis of a temperature of water discharged from the water-refrigerant heat exchanger and a condensation temperature of the first refrigerant cycle, while only the first compressor is driven, characterized in that when a first difference value between the condensation temperature of the first refrigerant cycle and a discharge water temperature of the water-refrigerant heat exchanger is greater than a first value, the first refrigerant cycle operates by driving of the first compressor only, wherein the condensation temperature is detected via a condensation temperature detector and the discharge water temperature is detected via a discharge water temperature detector. a first refrigerant cycle in which a first refrigerant circulates, and including a first compressor, an outdoor heat exchanger, and a first expansion device; a second refrigerant cycle, in which a second refrigerant circulates, and including a second compressor and a second expansion device; a water-refrigerant heat exchanger, to which the first refrigerant compressed in the first compressor and the second refrigerant compressed in the second compressor is introduced; a water introduction path coupled to a first side of the water-refrigerant heat exchanger and into which supplied water is introduced; and a water discharge path coupled to a second side of the water-refrigerant heat exchanger and from which the water heat-exchanged in the water-refrigerant heat exchanger is discharged; the method comprising: turning on the heat pump hot-water supply device and inputting a predetermined discharge water temperature; determining whether an outdoor air temperature is greater than a predetermined temperature; when the outdoor air temperature is greater than the predetermined temperature, driving only the first compressor, and when the outdoor air temperature is less than the predetermined temperature, driving the first and second compressors; and determining additional driving of the second compressor on the basis of a temperature of water discharged from the water-refrigerant heat exchanger and a condensation temperature of the first refrigerant cycle, while only the first compressor is driven, characterized in that when a first difference value between the condensation temperature of the first refrigerant cycle and a discharge water temperature of the water-refrigerant heat exchanger is greater than a first value, the first refrigerant cycle operates by driving of the first compressor only, wherein the condensation temperature is detected via a condensation temperature detector and the discharge water temperature is detected via a discharge water temperature detector. turning on the heat pump hot-water supply device and inputting a predetermined discharge water temperature; determining whether an outdoor air temperature is greater than a predetermined temperature; when the outdoor air temperature is greater than the predetermined temperature, driving only the first compressor, and when the outdoor air temperature is less than the predetermined temperature, driving the first and second compressors; and determining additional driving of the second compressor on the basis of a temperature of water discharged from the water-refrigerant heat exchanger and a condensation temperature of the first refrigerant cycle, while only the first compressor is driven, characterized in that when a first difference value between the condensation temperature of the first refrigerant cycle and a discharge water temperature of the water-refrigerant heat exchanger is greater than a first value, the first refrigerant cycle operates by driving of the first compressor only, wherein the condensation temperature is detected via a condensation temperature detector and the discharge water temperature is detected via a discharge water temperature detector.