This paper investigated the adaptive impulsive synchronization for a class of non-autonomous chaotic systems with unknown Lipschitz constant. Firstly, based on the Lyapunov stability theory, adaptive control theory and impulsive control theory, the adaptive controller, the impulsive controller and the parametric update law were designed respectively. Then, by the generalized Barbalat's lemma, the global asymptotic synchronization between the drive system and the response system was proved, and some corresponding sufficient conditions were also obtained. Two numerical examples were given to show the effectiveness of the proposed method.