This invention relates to an in-ash unburned component estimating device for a coal-fired furnace which monitors the density of in-ash unburned component contained in burning waste gases to operate the furnace efficiently. The object of the invention is to infer and estimate from the current situation by a simple means the density of in-ash unburned component in the burning exhaust gases that affects the combustion efficiency. A furnace temperature, a load band in the furnace, a furnace contamination coefficient, a ratio of two-stage combustion air supplied to the furnace, and a coal mixture ratio are taken in as fuzzy quantities to infer fuel ratio data and correction data used to correct predetermined reference values of reference in-furnace temperature distribution, reference in-furnace air ratio distribution and reference powdered coal grain diameter distribution. The reference values corrected by the correction data and coal reaction rate data determined from the fuel ratio data are used to calculate the density of in-ash unburned components in the burning waste gases.