Based on computational fluid dynamics, the debris flow is considered as a one-dimensional, laminar, unsteady flow down a steep slope with Herschel-Bulkley rheological model, and the conservation of mass and momentum are integrated along the depth of plug zone and shear zone, respectively. In addition, the mathematical model is improved by analyzing the mainly influencing factors of debris flow and adding the drag force and earth pressure coefficient into the depth-averaged equations. The Lagrange difference method is used to solve the partial differential equations in this paper. the model can reproduce the motion of debris flow with a level of accuracy by comparing the results of two simple cases.