A filtration device for treating wastewater by an up-flow biological filtration process, the device comprising: a distribution channel for distributing a wastewater vertically upward or for discharging backwash water, received vertically downward, to the outside; a reaction tank, into which the wastewater distributed from the distribution channel flows, comprising at least two types of flotation filter media (134, 138) having different sizes and having a lower specific gravity than water, a treated water storage tank for receiving the treated water from which solids and organics are removed through the filter media (134, 138) and discharging it to the outside or discharging the backwash water flowing in from the outside to the filter media (134, 138), a strainer block separating the reaction tank and the treated water storage tank, and comprising at least one nozzle having a plurality of outlets smaller than the filter media (134, 138) that let air or liquid pass through but not the filter media (134, 138), so as to receive the treated water from the reaction tank and introduce it in the treated water storage tank or so as to spray the backwash water from the treated water storage tank into the reaction tank, wherein when the wastewater is distributed vertically upward from the distribution channel the filter media (134, 138) ascend together with the wastewater up to the height at which the strainer block is located, said strainer block preventing the filter media (134, 138) from ascending further and leading them to clump together and to separate according to their size, allowing the filter media (134, 138) to remove solids and organics in the wastewater, wherein the filter media having a relatively larger size receive a greater buoyancy than the filter media having a relatively smaller size by the wastewater distributed vertically upward by the distribution channel, so that the filter media having relatively smaller size is disposed at relatively lower end of reaction tank and the filter media having relatively larger size is disposed at relatively upper end of the reaction tank, wherein the filter media having a relatively smaller size removes solids and the filter media having a relatively larger size removes fine solids and dissolved organics in the wastewater using aerobic microorganisms grown on its surface, wherein when the backwash water discharged from the treated water storage tank flows in vertically downward into the reaction tank, the filter media (134, 138) descend and are cleaned by removing the attached solids and organics. a distribution channel for distributing a wastewater vertically upward or for discharging backwash water, received vertically downward, to the outside; a reaction tank, into which the wastewater distributed from the distribution channel flows, comprising at least two types of flotation filter media (134, 138) having different sizes and having a lower specific gravity than water, a treated water storage tank for receiving the treated water from which solids and organics are removed through the filter media (134, 138) and discharging it to the outside or discharging the backwash water flowing in from the outside to the filter media (134, 138), a strainer block separating the reaction tank and the treated water storage tank, and comprising at least one nozzle having a plurality of outlets smaller than the filter media (134, 138) that let air or liquid pass through but not the filter media (134, 138), so as to receive the treated water from the reaction tank and introduce it in the treated water storage tank or so as to spray the backwash water from the treated water storage tank into the reaction tank, wherein when the wastewater is distributed vertically upward from the distribution channel the filter media (134, 138) ascend together with the wastewater up to the height at which the strainer block is located, said strainer block preventing the filter media (134, 138) from ascending further and leading them to clump together and to separate according to their size, allowing the filter media (134, 138) to remove solids and organics in the wastewater, wherein the filter media having a relatively larger size receive a greater buoyancy than the filter media having a relatively smaller size by the wastewater distributed vertically upward by the distribution channel, so that the filter media having relatively smaller size is disposed at relatively lower end of reaction tank and the filter media having relatively larger size is disposed at relatively upper end of the reaction tank, wherein the filter media having a relatively smaller size removes solids and the filter media having a relatively larger size removes fine solids and dissolved organics in the wastewater using aerobic microorganisms grown on its surface, wherein when the backwash water discharged from the treated water storage tank flows in vertically downward into the reaction tank, the filter media (134, 138) descend and are cleaned by removing the attached solids and organics.