Abstract: By use of the transformation between relative coordinates and absolute coordinates presented in this paper, the calculation of a Lyapunov exponential spectrum on a two-degree-of-freedom vibro-impact system with two-sided rigid stops was discussed by introducing Poincare mapping composed by flow mapping and local mapping and then changing the continuous-time dynamical system into the discrete-time counterpart. Comparing the diagram of Lyapunov exponential spectrum obtained by our algorithm with the diagram of global bifurcation for the given system, the validity of computing the spectrum of Lyapunov exponents with presented method was verified. Furthermore, some dynamical characters of this system under given parameters were obtained.