In this paper, numerical simulations of the heat transfer in molten-slag flow with free surface and phase change (solidification) is carried out, and we propose a new evaluation method for discharging performance of the molten-slag from coal gasifier. A stable operation of the coal gasifier requires that the molten-slag should be discharged from the slag-hole continuously. In the maintenance of discharging a molten slag, it is necessary to keep the molten-slag temperature higher than an ash fluid temperature, and to hold the fluidity of the molten-slag. From the viewpoint of gasification performance, if the air ratio is set low in order to raise the cold gas efficiency, the molten-slag is not able to get enough heat for its discharge, because of the lowering of gas temperature in the coal gasifier. To strike a balance between the maintenance of continuity on the molten-slag discharge and the improvement in gasification performance, it is important to develop a prediction and evaluation method for discharge performance of the molten-slag from coal gasifier.