Disclosed is a multi-cyclone dust separating apparatus, comprising a cyclone body, a top cover and a discharge cover. The cyclone body includes a main cyclone and a plurality of cyclone cones communicating with the main cyclone and arranged around a lower part of the main cyclone, each of which has a reverse conical shape whose diameter is reduced as approaching the top end thereof. The top cover is fitted on the top of the cyclone body and has an air inflow port introducing ambient air into the main cyclone. The discharge cover is fitted on the bottom of the main cyclone and collects and discharges the air discharged from the plurality of cyclone cones. Most of the air introduced into the top of the main cyclone through the air inflow port is discharged to the bottom of the main cyclone without being reversed to flow upwardly and then introduced into the plurality of cyclone cones.