Abstract: The calculation of a Lyapunov exponential spectrum on an impact damper vibration system is discussed by introducing Poincaré mapping in the rigid constraint section and by transforming the continual dynamic system to the discrete counterpart. The global parameters-varying rules of the Lyapunov exponential spectrum on this system are analyzed by numerical simulations. Comparing the Lyapunov exponential spectrum diagram with the global bifurcation diagram, validity and feasibility of this method of analyzing system stabilities using the Lyapunov exponential spectrum diagrams are verified. Some nonlinear characteristics under relevant parameters of the impact damper are also given in the paper.