A cyclone dust-collector which filters out dust and dirt from drawn-in air at least two times, comprising a multiple cyclone unit having a first cyclone and a plurality of second cyclones arranged at the outside of the first cyclone, for centrifugally separating the dust and dirt from the drawn-in air; a cover unit connected to the upper portion of the multiple cyclone unit, for allowing the first and the second cyclones to separating communicate with each other; and a dirt-collecting unit connected to the lower portion of the multiple cyclone unit, for collecting therein the dust and dirt centrifugally separated.