Slope failure is one of the failure modes of natural dams. Turbid seepage flow is often observed on the downstream slope of a natural dam in the field and indicates the migration of fine particles in the dam. However, the coupling of internal erosion and seepage in natural dams during the impounding process is still unclear. This paper studies fine particles migration in a dam and the slope failure mode in the laboratory. Then, a coupling model was proposed with the fines migration equation, unsaturated seepage flow equation, and local stability analysis equation. In addition to the variation in the permeability coefficient due to fine particles migration, the strength parameters and density of the soil are also changed, which is considered in the model. Based on the conditions of the laboratory tests, simulations were conducted with the coupling model, and some parameters, such as pore pressure, porosity, principle stress, and factor of safety, were analyzed. Meanwhile, the influence of internal erosion and seepage on the stability of dams under different conditions is studied. Furthermore, the influence of some model parameters on the internal structure of the dam and its stability are discussed.