PURPOSE:To provide the title gasifier having a slag discharge hole which is adapted so that the slag may be prevented from being deposited on and grown around it in order to avoid the stoppage of such a hole occasionally occurring in an entrained bed coal gasifier having a slag discharge hole on the bottom. CONSTITUTION:The lower part of a slag discharge hole 6 is surrounded by a water-cooled jacket 10 protruding beyond the inner surface of the refractory. The jacket 10 has a cylindrical or conical form, and cooling water passes it through pipes 11 and 12. The molten slag formed in the combustion furnace and flowing down into the slag discharge hole is rapidly cooled by contact with the jacket 10 to form brittle rapidly cooled slag, which hangs, then breaks near its upper support and falls.