A melt-slag gasifier with slag discharging device relates to a melt-slag gasifier. In the prior art, a slag-tapping port of a gasifier is easily blocked by slags and accordingly the gasifier cannot smoothly discharge slags, and there is the problem that the gasification surface cannot normally operate because of burning loss of a quenching ring at the slag-tapping port of the entrained flow gasifier and a downcomer. The interior of the melt-slag gasifier is successively divided into a combustion chamber and a quenching chamber from top to bottom; a water cooling coil is disposed in the melt-slag gasifier body, and forms a conical barrel through coiling of a water cooling pipe from top to bottom, the top end of the water cooling coil is disposed in the combustion chamber, the bottom end of the water cooling coil is disposed in the quenching chamber, the combustion chamber and the quenching chamber are communicated through the water cooling coil, the outer wall at the top end of the water cooling coil is provided with a notch, and an annular melt-slag storage groove is formed between the outer wall of the water cooling coil and the inner wall at the bottom of the combustion chamber; and the downcomer is disposed in the quenching chamber, the upper end of the downcomer is communicated with the water cooling coil, and the lower end of the downcomer is inserted into cooling water of the quenching chamber. The device is applied to the field of coal gasification.