@ A dust preheating system with a preliminary calcination furnace for powdery material, including a preheater having a plural number of dust separators connected one after another in a vertical direction to form a corresponding number of preheating stages, a preliminary calcination furnace located between the preheater and a combustion furnace when seen in the flow direction of the powdery material and connected through a combustion air duct to a clinker cooler located on the downstream side of the combustion furnace, the preliminary calcination furnace being provided with an independent fuel feeder and connected through a combustion gas duct to the lowermost dust separator for calcined material, the second lowest one of the dust separators of the preheater having the dust outlet thereof connected to the preliminary calcination furnace, and the lowermost dust separator having a calcined dust outlet connected to an inlet of the combustion furnace, characterised in that: at least the second lowest one of the dust separators is constituted by a cyclone separator having an opening in the side wall thereof and having a fine dust outlet at the bottom end thereof; and a pocket for the coarse dust hermetically connected to the opening and having a coarse dust outlet at the bottom end thereof; the fine and coarse dust outlets being connected to fine and coarse dust feed ports provided at spaced positions in the side wall of the preliminary calcination furnace.