To provide a melting furnace for incinerated ash or land-fill refuse capable of continuously stably discharging molten slag in a melting furnace for melting incinerated ash or land-fill refuse.

A melting furnace is provided, in which incinerated ash or land-fill refuse and coke is or are supplied into a shaft furnace, and a residue produced through thermal decomposition under the atmosphere less than the stoichiometric amount of air with respect to a combustible substance is discharged to the outside of the furnace as molten slag. In the melting furnace, a coke layer is formed at a furnace bottom, and a plasma torch is provided so as to blow hot air toward the coke layer, and further the furnace bottom is positive pressure not higher than the average value of 5 KPa.