To provide a heat pump heat source system prevented in the overheating of a heat pump when performing a heating operation by performing heat radiation to hot water in a hot water storage tank and continuing the operation of the heat pump.

A heating execution prediction part 154 predicts whether or not a first heating operation is executed within a prescribed time. When it is predicted that the first heating operation is executed within the prescribed time by the heating execution prediction part 154, a boil-up temperature setting part 155 sets a heating priority temperature at which the heat radiation to the hot water in the hot water storage tank 11 from a heat pump heat medium in a heat pump heat exchanger 55 can be performed to a boil-up temperature of the hot water in the hot water tank 11 in a heating-off state, and when it is not predicted that the first heating operation is executed within the prescribed time, sets the hot water prior temperature not lower than a set hot water temperature to the boil-up temperature.