A multi-cyclone dust separating apparatus includes: a multi-cyclone unit including a first cyclone chamber body having a first cyclone chamber and at least one protection chamber formed around at least a portion of an outer circumference of the first cyclone chamber, and at least one secondary cyclone chamber body disposed in the protection chamber, each secondary cyclone chamber body having at least one secondary cyclone chamber; a cover unit connecting an upper end of the multi-cyclone unit and guiding air discharged from the first cyclone chamber to the at least one secondary cyclone chamber; a dirt collecting unit adapted to connect to a lower end of the multi-cyclone unit and configured to collect dirt separated from the air in the first and secondary cyclone chambers; and an air discharge duct configured to discharge air that has passed through the multi-cyclone unit.