As floods often occur in steep terrain and water flow changes rapidly, the calculated values in two-dimensional numerical simulations of flash flood disasters are unstable and even the calculation diverges in the simulation. To solve these problems, we present a grid outflow correction method, which is based on the leap-frog finite difference format. Through circular modification of the outflow rate of the grid, this method ensures mass conservation over the whole process of computation and improves the stability of numerical calculation. While using the local dam bursting model, we conducted mass conservation comparison between the simulated result of the grid outflow correction method and that of the algorithm of the implicit alternating direction. The results show that the grid outflow correction method can ensure simulation accuracy and numerical stability under the conditions of steep terrain and a moving boundary. Based on the proposed method, simulation of the process of the extreme flash flood disaster that occurred in 2010 in Zhouqu County, in Gansu Province was carried out. The comparison of simulation results and the results of remote sensing estimation after the disaster shows that the deviation of the flood evolution time, speed, and impact height were within ±5%, and the evolution path was consistent.