A fluidized-bed classification apparatus for removing a foreign matter by settling the foreign matter from a mixture of a fluidized medium for forming a fluidized bed and the foreign matter mixed with the fluidized medium, the foreign matter being incompetent to the formation of the fluidized bed, the apparatus comprising: a coarse classification section configured to remove a foreign matter having a relatively large size and a foreign matter having a large specific gravity; a fine classification section configured to further remove a foreign matter from the mixture from which the foreign matters have been removed in the coarse classification section; a partition wall that partitions the coarse classification section and the fine classification section; a first fluidizing-air supply floorboard (7, 8) configured to supply a fluidizing air into the coarse classification section; and a second fluidizing-air supply floorboard configured to supply a fluidizing air into the fine classification section; wherein the second fluidizing-air supply floorboard is inclined downward toward the coarse classification section, and an inclination angle of the second fluidizing-air supply floorboard is uniform or increases as a location on the second fluidizing-air supply floorboard comes closer to the coarse classification section, wherein the first fluidizing-air supply floorboard (7,8) comprises a lower fluidizing-air supply floorboard and an upper fluidizing-air supply floorboard located higher than the lower fluidizing-air supply floorboard, wherein a discharge port is provided between the upper fluidizing-air supply floorboard and the lower fluidizing-air supply floorboard, the discharge port being configured to discharge the foreign matters removed in the coarse classification section and the fine classification section, and wherein the partition wall is located right above a boundary between the lower fluidizing-air supply floorboard and the second fluidizing-air supply floorboard. a coarse classification section configured to remove a foreign matter having a relatively large size and a foreign matter having a large specific gravity; a fine classification section configured to further remove a foreign matter from the mixture from which the foreign matters have been removed in the coarse classification section; a partition wall that partitions the coarse classification section and the fine classification section; a first fluidizing-air supply floorboard (7, 8) configured to supply a fluidizing air into the coarse classification section; and a second fluidizing-air supply floorboard configured to supply a fluidizing air into the fine classification section; wherein the second fluidizing-air supply floorboard is inclined downward toward the coarse classification section, and an inclination angle of the second fluidizing-air supply floorboard is uniform or increases as a location on the second fluidizing-air supply floorboard comes closer to the coarse classification section, wherein the first fluidizing-air supply floorboard (7,8) comprises a lower fluidizing-air supply floorboard and an upper fluidizing-air supply floorboard located higher than the lower fluidizing-air supply floorboard, wherein a discharge port is provided between the upper fluidizing-air supply floorboard and the lower fluidizing-air supply floorboard, the discharge port being configured to discharge the foreign matters removed in the coarse classification section and the fine classification section, and wherein the partition wall is located right above a boundary between the lower fluidizing-air supply floorboard and the second fluidizing-air supply floorboard. wherein the second fluidizing-air supply floorboard is inclined downward toward the coarse classification section, and an inclination angle of the second fluidizing-air supply floorboard is uniform or increases as a location on the second fluidizing-air supply floorboard comes closer to the coarse classification section, wherein the first fluidizing-air supply floorboard (7,8) comprises a lower fluidizing-air supply floorboard and an upper fluidizing-air supply floorboard located higher than the lower fluidizing-air supply floorboard, wherein a discharge port is provided between the upper fluidizing-air supply floorboard and the lower fluidizing-air supply floorboard, the discharge port being configured to discharge the foreign matters removed in the coarse classification section and the fine classification section, and wherein the partition wall is located right above a boundary between the lower fluidizing-air supply floorboard and the second fluidizing-air supply floorboard.