Heat pump hot-water supply system and control method thereof

Provided is a heat pump hot-water supply system capable of preventing smudgily from clinging to the utmost and improving maintenance by setting an argentum ion generating device on a hot-water accumulation path of a bathtub, and a control method of the heat pump hot-water supply system. The heat pump hot-water supply system includes: a heat pump unit (10) configured to connect a compressor (11), a cold water heat exchanger (12), an expansion valve (13) and an air heat exchanger (14) by a pipeline in sequence; a hot-water tank (31), to store high-temperature water generated by the cold water heat exchanger (12); the bathtub (50), to which the high-temperature water and cold water are supplied by a funnel (34) after mixing by a mixing pin (33); a hot-water insulating loop (40), composed of a bathing recycle pump (41) for hot-water circulation of the bathtub (50) and a bathing heat exchanger (42) for exchanging heat between the hot water and the high-temperature water; the argentum ion generating device (35), ar