Chaos and chaos synchronization of the centrifugal flywheel governor system are studied in this paper. By mechanics analyzing, the dynamical equation of the centrifugal flywheel governor system are established. Because of the non-linear terms of the system, the system exhibit both regular and chaotic motions. The evolution from Hopf bifurcation to chaos is shown by the bifurcation diagrams and a series of Poincaré sections under different sets of system parameters, and the bifurcation diagrams are verified by the related Lyapunov exponent spectra. This paper addresses control for the chaos synchronization of feedback control laws in two coupled non-autonomous chaotic systems with different coupling terms, which is demonstrated and verified by Lyapunov exponent spectra and phase portraits. Finally, numerical simulations are presented to show the effectiveness of the proposed chaos synchronization scheme.