An adaptive control scheme is developed to study the generalized adaptive chaos synchronization with uncertain chaotic parameters behavior between two identical chaotic dynamic systems. This generalized adaptive chaos synchronization controller is designed based on Lyapunov stability theory and an analytic expression of the adaptive controller with its update laws of uncertain chaotic parameters is shown. The generalized adaptive synchronization with uncertain parameters between two identical new Lorenz-Stenflo systems is taken as three examples to show the effectiveness of the proposed method. The numerical simulations are shown to verify the results.