The invention relates to a method for treating water laden with pollutants for the purpose of making the water drinkable, said method including: an elimination step consisting of contacting said water laden with pollutants, within a stirred contact tank (2), with an active particulate material (19) using a predetermined concentration of the active particulate material (19) in said water; an extraction step consisting of continuously extracting from said contact tank (2) a mixture consisting of water and of active particulate material (19); a separation step consisting of continuously separating said active particulate material (19) from said mixture. According to the invention, the separation step consists in particular of feeding the mixture of water and active particulate material into a filter drum (4).