The existence of special piecewise-linear structure, global linear amplitude adjuster and phase-reverse controller in improved chaotic system with constant Lyapunov exponent spectrum contributed much to finding new synchronization methods and new adjusting parameters. According to the principle of generalized synchronization, by constructing appropriate driving system and response system, generalized synchronization of the improved chaotic system with constant Lyapunov exponent spectrum then can be achieved. By changing the parameter of response system, the complete synchronization and generalized projective synchronization can be further realized. The amplitude of the state variable of the driving system and the response system can be controlled to increase and decrease synchronously by the global linear amplitude adjuster, while the phase of certain variables can be controlled to reverse synchronously by the phase-reverser. This synchronization system dispenses with other special controllers, possesses simple structure and so can be implemented easily. Finally, the implement circuit of synchronization system is designed. It is validated by experiment simulation that the synchronization methods are feasible, the amplitude and the phase of the state variable in the synchronization system can be controlled by special parameters of the improved chaotic system.