Numerical modeling of the combustion of a lean methane-air mixture containing fine coal particles entering the “Swiss-roll” type recuperative burner is considered. The mathematical model is constructed under the following assumptions: the flow field is two-dimensional; the gas mixture is an ideal incompressible gas consisting of oxygen, methane, coal volatile substances, carbon monoxide, carbon dioxide, water vapor, hydrogen and nitrogen. In the gas phase four oxidation reactions, in which methane, volatile matter of coal, carbon monoxide, hydrogen participate and the reaction of carbon dioxide decomposition take place. On the surface of the coal particle, there are three oxidation reactions involving oxygen, carbon dioxide and water vapor, resulting in the formation of carbon monoxide. It is assumed that coal contains 8% of ash, 12.9% of volatile substances and 79.1% of carbon. It is shown that for a two percent methane-air mixture the reaction zone shifts toward the center of the burner as the feed rate of the mixture increases. An increase in the content of coal particles leads to a shift of the reaction zone into the inlet part of the burner, and the heat release in the burner increases.