To provide a secondary combustion control device of a garbage incinerator which is capable of effectively reducing the concentration of carbon monoxide and nitrogen oxide contained in an exhaust gas, and extensive in controllable range.

The fluctuation range of the oxygen concentration is divided into a plurality of oxygen concentration area including an appropriate oxygen concentration area. In this area, the concentration of nitrogen oxide and the concentration of carbon monoxide contained in an exhaust gas after the secondary combustion are simultaneously reduced, a fuzzy inference part 6 in which a specified process data obtained from a garbage incinerator is an input data and the oxygen data belonging to the oxygen concentration area is an output data is provided for each oxygen concentration area, and, if the output of a first fuzzy inference part 6a corresponding to the appropriate oxygen concentration area is within the appropriate oxygen concentration area, a target oxygen concentration setting means 8 sets the output as the target oxygen concentration. If the output of the first fuzzy inference part 6a is outside the appropriate oxygen concentration area, a specified corrective operation is effected to the output of other fuzzy inference part 6 corresponding to other oxygen concentration area to which the output belongs to set the target oxygen concentration.