A cyclone dust separating apparatus for separating dust from external air drawn in thereto and discharging the separated dust, comprises at least one first cyclone body having a tubular shape and forming a first cyclone chamber where the external air is rotated; and at least one second cyclone body forming a second cyclone chamber where the air discharged from the first cyclone chamber is rotated again to separate dust, wherein the external air is drawn in through a lower end of the first cyclone chamber and discharged through an upper end of the first cyclone chamber, and the air discharged from the first cyclone chamber is drawn in through an upper end of the second cyclone chamber and discharged through an upper end of the second cyclone chamber.