A filter dust collector is disclosed. The filter dust collector includes a housing, filter cloths fixed to an inside of the housing, a filter body part disposed inside the housing and having filter insertion holes, a compressed air supply part coupled to peripheries of the filter insertion holes, a transfer part connected to the filter body part to move the filter body part and the compressed air supply part in a longitudinal direction, a duct suction port formed on a side surface of the housing to suck air to be filtered, a supply port formed on a side surface of the housing to discharge filtered air, and a dust discharge port formed on a side surface of the housing, wherein the filter cloths are positioned at the filter insertion holes, the filter body part and the compressed air supply part move in the longitudinal direction, and the compressed air supply part sprays compressed air to the filter cloths.