The discrete element method (DEM) is extensively used in the investigation of granular systems and the particle shape has a great influence on the dynamics behaviors of granular material. To describe some kinds of non-spherical particles accurately, a multi-super-ellipsoid model, somewhat similar to the multi-sphere model, is proposed in this paper. With this model, non-spherical particles are modeled by connecting a certain number of super-ellipsoids, and the component super-ellipsoids can overlap with each other. Some non-spherical particles, such as tablets and capsules, can be described accurately by the multi-super-ellipsoid model. To verify the accuracy of the multi-super-ellipsoid model, four kinds of non-spherical particles including three kinds of tablets and one kind of capsule, are adopted in this research. The packing of four kinds of non-spherical particles in a cylinder container and the flow of three kinds of tablets in a horizontal rotating drum are done by both numerical simulation and experiment, and the simulation results are compared with the corresponding experiments. The results show that the simulation can predict the basic characteristics of such kinds of non-spherical particles accurately, including fill heights and the dynamic angles of repose, which show that the accuracy of the multi-super-ellipsoid model is quite high. The computational efficiency of the new model is also tested, and the results indicate that the computational efficiency depends on the particle shape and the number of sub-particles in the composite particle. (C) 2019 Elsevier B.V. All rights reserved.