Coordination number is an important microscopic parameter in describing the packing of particles. However, little information is available for particle mixtures because of the difficulty of investigating them experimentally. This article presents a numerical study on the coordination numbers of a ternary packing system with size ratios of 24.4/11.6/6.4 by means of the discrete element method (DEM). Good agreement between the simulated and measured results was obtained, which confirms, at a particle scale, that DEM is capable of generating reliable results for structural analysis of particle packing. It was also found that the coordination number distribution of each of the cases considered can be described by the so-called Johnson S-B function. The distribution parameters of the function were quantified based on the DEM simulation results so that the coordination number distributions corresponding to different contact types in this ternary packing system can be fully described.