A belt pressure filter comprises a gravity dewatering zone for dewatering a sludge as a function of the gravity and a forced dewatering zone for a forced dewatering of the sludge by means of external pressure. An endless filter belt travels from the gravity dewatering zone to the forced dewatering zone. The coagulated sludge is supplied onto the filter belt by means of the gravity dewatering zone. Information representing the level of the sludge deposited on the belt is obtained as an information concerning the dewatering ability of the coagulated sludge supplied onto the filter belt. The traveling speed of the filter belt is calculated and controlled on the basis of the above described level information which represents the layer thickness and hence also the solids concentration. The optimum amount of a dosage of a coagulating agent is determined based on the traveling speed of the filter belt as calculated. As a result, the water content in a dewatered cake is maintained low and constant, while an optimal amount of coagulating agent most suited to the sludge characteristics at that time is added to the material without wasting any excess coagulating agent.