In this paper, a new three-dimensional autonomous chaotic system is constructed by adding a product term with variable coefficient to the first equation of Chen's system. The new system with different groups of coefficients can be chaotic or not by adjusting the variable coefficient, that is, by adjusting the variable coefficient, chaos occurs in new system when Chen's system is not chaotic, or chaos is suppressed in new system even if Chen's system is chaotic. The characteristics of the new chaotic system are analyzed in detail and the synchronization of new system is considered. Moreover, the simulation results are also presented.