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In this paper, a depth-averaged numerical model is proposed to simulate the propagation of debris flows. To understand the dynamical features of debris flows, the granular-liquid mixture model is employed, where the resistance of liquid constituent consisting of water and fine particles is described by Herschel-Bulkley rheology, and the resistance of granular constituent involving the coarse particles is formulated by the Voellmy model. An Eulerian leapfrog finite difference scheme is employed to numerically solve the governing equations of debris flows. Several idealized dam break problems are numerically implemented to test the accuracy and stability of the numerical scheme, and good agreement with the analytical solutions is found. Furthermore, the experiment carried out by Iverson (2010) is numerically implemented in this study to validate the proposed model, and the results are in good agreement. Then, a typical debris flow in Tianmo gully in Tibet, China, is numerically analyzed based on the proposed model. The results show that several details of the motion of debris flows over a real terrain can be accurately predicted by the proposed model. The comparisons between the basal Coulomb friction model and the Voellmy model show that the mobility of debris flows can be overestimated when only the Coulomb friction model is employed. An analysis based on the unsteady motion of a uniform mass indicates that Voellmy resistance can rescue the issue in regard to the absence of resistance of the granular component due to fully liquefied states. Finally, the influence of the rheology of liquid slurry on the motion of debris flows is analyzed, and the results demonstrate that the basal resistances caused by the liquid slurry were very small relative to the basal resistances caused by granular constituent. [ABSTRACT FROM AUTHOR]