A burner for combusting particulate fuels comprises a combustion chamber fitted with a plurality of grates stacked in stairstep fashion, each having a downwardly sloping surface over which the fuel flows continuously as it burns. The grates may be horizontally adjustable to change the downward slope of the flowing fuel. Each grate rests upon supports projecting from opposite side walls of the burner. The supports extend beyond the downwardly sloping surfaces of the grates and beyond the forward edge of the fuel bed so that the flow of fuel is diverted by the supports away from the side walls of the firebox, creating air passages which allow air to flow directly to the flame. The burner is fitted with a hopper for receiving and containing the fuel with a baffle plate depending from it shaped to distribute the fuel across the width of the grate in a manner which promotes the flow of the fuel. Tubular channels are positioned below the lowermost grate so that air is supplied to any unburned fuel accumulating at the bottom of the incinerator.