This paper deals with the open problem of the global boundedness of the Chen system based on Lyapunov stability theory, which was proposed by Qin and Chen (2007). The innovation of the paper is that this paper not only proves the Chen system is global bounded for a certain range of the parameters according to stability theory of dynamical systems but also gives a family of mathematical expressions of global exponential attractive sets for the Chen system with respect to the parameters of this system. Furthermore, the exponential rate of the trajectories is also obtained.