The dust concentration of the flue gas leaving an electrostatic precipitator and introduced into an absorption tower of a desulfurizer is adjusted to a level of 100 to 500 mg/Nm.sup.3. At the same time, a dust slurry having a higher dust concentration is separated and withdrawn from the slurry within the aforesaid absorption tower, and then subjected to a solid-liquid separation treatment. Thus, solid matter containing dust at a high concentration is extracted and discharged out of the system of the desulfurizer.