Based on the Lyapunov stability theory and nonlinear dynamic theory, a controller is designed, the control of complete synchronization and anti-phase synchronization between 3-dimensional and 4-dimensional chaotic systems with different structures is implemented, and the two kind of synchronization are respectively proved strictly in mathematics. In this paper, taking a new 3D autonomous system for example, hyper-chaotic system is achieved by introducing an additional state variable to the new 3D chaotic system, thus a complete synchronization and anti-phase synchronization between chaotic systems with different structures and dimensions are investigated. Finally, by the Runge-Kutta scheme numerical simulation and from the simulation analysis of the error system between driving and coupled system, the graph of the errors can show that errors will become zero in short time, the numerical simulation shows the validity of the theoretical analysis and the effectiveness of the proposed method.