A heat pump-type heating and hot-water supply apparatus comprising: a refrigerant circuit including a compressor, a water/refrigerant heat exchanger configured to exchange heat between refrigerant and water, and a heat source side heat exchanger; a hot-water supply circuit including a circulation pump and being configured to circulate hot water between a heating terminal (40, 70) and the water/refrigerant heat exchanger; going temperature detection means configured to detect a going temperature (Tg) being the temperature of water flowing out of the water/refrigerant heat exchanger; outside temperature detection means provided in the vicinity of the heat source side heat exchanger configured to detect an outside temperature and control means configured to control the compressor so that the going temperature (Tg) approaches to a target temperature (Tt) in accordance with a set temperature of the heating terminal (40, 70), characterized in that the control means when decreasing the speed of the compressor to decrease the going temperature (Tg), judges whether or not the going temperature (Tg) is equal to or more than an upper limit temperature higher by a given temperature than the target temperature (Tt), in the case that the speed of the compressor is at or below a lower limit speed (Rd) lower than an optimum speed (Rm) corresponding to the highest value of the COP at the outside temperature, stops the compressor in the case that the going temperature (Tg) is equal to or more than the upper limit temperature, and continues to operate the compressor at the lower limit speed (Rd) in the case that the going temperature (Tg) is not equal to or more than the upper limit temperature. a refrigerant circuit including a compressor, a water/refrigerant heat exchanger configured to exchange heat between refrigerant and water, and a heat source side heat exchanger; a compressor, a water/refrigerant heat exchanger configured to exchange heat between refrigerant and water, and a heat source side heat exchanger; a hot-water supply circuit including a circulation pump and being configured to circulate hot water between a heating terminal (40, 70) and the water/refrigerant heat exchanger; going temperature detection means configured to detect a going temperature (Tg) being the temperature of water flowing out of the water/refrigerant heat exchanger; outside temperature detection means provided in the vicinity of the heat source side heat exchanger configured to detect an outside temperature and control means configured to control the compressor so that the going temperature (Tg) approaches to a target temperature (Tt) in accordance with a set temperature of the heating terminal (40, 70), when decreasing the speed of the compressor to decrease the going temperature (Tg), judges whether or not the going temperature (Tg) is equal to or more than an upper limit temperature higher by a given temperature than the target temperature (Tt), in the case that the speed of the compressor is at or below a lower limit speed (Rd) lower than an optimum speed (Rm) corresponding to the highest value of the COP at the outside temperature, stops the compressor in the case that the going temperature (Tg) is equal to or more than the upper limit temperature, and continues to operate the compressor at the lower limit speed (Rd) in the case that the going temperature (Tg) is not equal to or more than the upper limit temperature.