Landslide dams are formed by the blockage of rivers with landslides, or any debris flows. Such dams are prone to failure and therefore, simulation of their failure and induced morphological changes is of great importance for hazard mitigation. Multi-layer and non-uniform sediments are usually observed in landslide dam materials, but these are rarely considered in simulations. In this paper, a two-dimensional numerical model considering multi-layered and non-uniform sediments is proposed. The model solves the shallow water equations, the Exner equation considering the different size fractions and Hirano's active layer equation based on a finite volume scheme in a weakly coupled approach. Two experimental tests are used to assess the applicability and accuracy of the model. The results show that it can well simulate the flow and morphological changes, as well as the surface coarsening and fining phenomena related to multi-layer and non-uniform sediments. The numerical results of dam failure process and morphological changes are in overall good agreement with the experiments, but the peak discharge and bed elevation tend to be underestimated when finer material is considered. Finally, the influence of sediments fractions and active layer depth on numerical results, as well as the limitations of the model are discussed.