By differentiating the parameters of a newly proposed chaotic system with invariable Lyapunov exponent spectrum, an improved chaotic system is reported in this paper. The system has three important properties which can be summarized as: invariable Lyapunov exponent spectrum for two parameters, existence of the global linear amplitude adjuster and the phase reversal parameter. Simulation analysis by Lyapunov exponent spectrum and bifurcation diagram combined with theoretical reasoning and theory proving, the dynamical characteristics of the system are investigated and expounded. An analog electronic circuit is designed to implement the improved system, and then the chaotic behavior is verified by physics experiments. Finally, the synchronization of the new chaotic system is realized by using the single variable coupling feedback, and meanwhile the circuit of synchronization is presented and the synchronization condition is verified.