Method for treating water by filtration on a granular bed in order to reduce its content in contaminants, said method comprising the steps for: - making a water to be treated travel in transit in a reactor containing said bed in an upward flow at a speed that does not permit the fluidization of said bed but permits said material to migrate, as and when the filtration takes place, towards the lower part of said reactor, said reactor being provided in its upper part with means for introducing said water to be treated; - continuously removing a fouled granular material at the foot of the reactor with the help of cleaning means providing within the reactor and including an helicoidal ramp, by means of a piping into which a gas is insufflated, said fouled granular material being constituted by granular material and contaminants adsorbed on said granular material and by particles retained by said granular material; - continuously or intermittently carrying out the physical cleansing of said fouled granular material thus removed, so as to obtain a cleansed granular material essentially rid of said contaminants; - reinjecting the granular material thus cleansed into said bed; characterized in that said granular material is an adsorbent granular material and in that the method comprises: a continuous or intermittent step for the discharging, during the filtration, of a part of said fouled granular material removed at the foot of the reactor performed by drawing out said part from said piping, this piping being external to the body of said reactor; and a continuous or intermittent step for the introduction into said reactor, during the filtration, of fresh granular material in a quantity sufficient to compensate for said part of granular material discharged; - making a water to be treated travel in transit in a reactor containing said bed in an upward flow at a speed that does not permit the fluidization of said bed but permits said material to migrate, as and when the filtration takes place, towards the lower part of said reactor, said reactor being provided in its upper part with means for introducing said water to be treated; - continuously removing a fouled granular material at the foot of the reactor with the help of cleaning means providing within the reactor and including an helicoidal ramp, by means of a piping into which a gas is insufflated, said fouled granular material being constituted by granular material and contaminants adsorbed on said granular material and by particles retained by said granular material; - continuously or intermittently carrying out the physical cleansing of said fouled granular material thus removed, so as to obtain a cleansed granular material essentially rid of said contaminants; - reinjecting the granular material thus cleansed into said bed; a continuous or intermittent step for the discharging, during the filtration, of a part of said fouled granular material removed at the foot of the reactor performed by drawing out said part from said piping, this piping being external to the body of said reactor; and a continuous or intermittent step for the introduction into said reactor, during the filtration, of fresh granular material in a quantity sufficient to compensate for said part of granular material discharged;