An ash melting furnace capable of a high-efficiency, stable operation and accommodating load variations, which is used for mixed melting for heating and melting main ash and flying ash as burned ash simultaneously, characterized in that main ash (coarse grain ash) in an upper layer and flying ash (fine grain ash) in a lower layer are supplied in layers from one end of the furnace body and heated and melted by a burner while being moved to the other end, whereby enabling the burner, when an oxygen enriched burner is used, to properly control an oxygen amount added to air (concentration change included) and, in response to a heated and melted ash condition caused by the combustion of the oxygen enriched burner, to properly control, in addition to fuel supply amount, an ash supply amount as required by a change in the oxygen enriching concentration.