In this paper, the dynamical behaviors of the centrifugal flywheel governor with external disturbance are discussed, and the system exhibits exceedingly complicated dynamic behaviors. The influence of system parameter on the chaotic system is discussed through Lyapunov-exponents spectrum and global bifurcation diagram, which accurately portray the partial dynamic behavior of the system. It is chaotic with proper system parameter, and we utilize Poincaré sections to study the Hopf bifurcation and chaos forming of the centrifugal flywheel governor system. Then, we utilize coupled-feedback control and adaptive control to realize the chaotic synchronization and obtain the conditions of chaos synchronization. Finally, we carry on the theory proof using the Lyapunov stability theory to the obtained conditions, the theoretical proof and number simulation shows the effectiveness of these methods.