In this paper, a class of wide range Julia set of parameter identification problem is investigated. Based on the nonlinear feedback controller and the discretized equation theory, the designed generally applicable adaptive synchronization controller and the parameter adaptive law are obtained, and it is proved that the designed controller of generalized Julia set can achieve the synchronization. Moreover, it can identify the unknown parameters of the generalized Julia set. Particularly, the parameter identification of the basic form of Julia set is discussed in the paper.