In this paper, the complete synchronization and antiphase synchronization between the 3dimensional chaotic system and 4dimensional hyperchaotic system with different dimension and fractional order are researched in which the fractionalorder Lü chaotic system and the fractionalorder Chen hyperchaotic system are as an example. First, Based on the fractional theory of stability and nonlinear dynamic theory. the nonlinear controller is designed, and by the nonlinear controller the complete synchronization and antiphase synchronization between different the 3D fractionalorder chaotic system and 4D fractionalorder hyperchaotic system with different dimension and fractional order are realized. Second, based on the fractionalorder theory of stability the two kind of synchronization are respectively proved strictly in mathematics. Finally, by the PredictorCorrector scheme numerical simulation, the validity of the method presented in this paper is verified.