Nonlinear dynamical behaviors of a train suspension system with impacts are investigated. The suspension system is described through an impact model with possible stick between a bolster and two wedges. The analytical conditions that reflect the motion mechanisms for the complex motion are given. The mapping structures for periodic and chaotic motions of such a system can be described. The analytical prediction of the complex motions can be conducted from the mapping structure, and numerical simulations for periodic and chaotic motions can be carried out in sequel.