Abstract: A control device for a heat pump system having a hot-water supply facility is disclosed which comprises an input device for inputting the cost of electricity for operating a heat pump and for inputting the cost of fuel for operating a boiler. A first sensor detects the temperature of the ambient air. A second sensor detects the moisture of the ambient air. A third sensor detects the temperature of the hot-water supply. An operation circuit selects an operation mode on the basis of the output signals received from the sensors. A comparison circuit selects the cheaper energy form based on cost data inputted from the input device in the heating air mode and in the hot-water supply mode. A control circuit selectively operates the heat pump or the boiler based on the result of the comparison performed by the comparison circuit.