Most of the approaches in numerical modeling techniques are based on the Eulerian coordinate system. This approach faces difficulty in simulating flash flood front propagation. This paper shows an alternative method that implements a numerical modeling technique based on the Lagrangian coordinate system to simulate the water of debris flow. As for the interaction with the riverbed, the simulation uses an Eulerian coordinate system. The method uses the conservative and momentum equations of water and sediment mixture in the Lagrangian form. Source terms represent deposition and erosion. The riverbed in the Eulerian coordinate system interacts with the flow of the mixture. At every step, the algorithm evaluates the relative position of moving nodes of the flow part to the fixed nodes of the riverbed. Computation of advancing velocity and depth uses the riverbed elevation, slope data, and the bed elevation change computation uses the erosion or deposition data of the flow on the moving nodes. Spatial discretization is implementing the Galerkin method. Furthermore, temporal discretization is implementing the forward difference scheme. Test runs show that the algorithm can simulate downward, upward, and reflected backward 1-D flow cases. Two-D model tests and comparisons with SIMLAR software show that the algorithm works in simulating debris flow.