This paper discusses the problem of the adaptive control of nonlinear impulsive differential dynamical systems. First, a class of adaptive controllers are designed for the nonlinear impulsive differential equations, where the nonlinear function can be decomposed into matching condition and mismatching condition. Second, combining with Lasalle invariant set theorem, Schur complement theorem and some inequality techniques, we consider the synchronization of impulsively coupled complex networks via the general adaptive control. Moreover, this paper proposes the pining adaptive synchronization results for impulsive dynamical complex networks. Finally, some examples with simulations are given to demonstrate the effectiveness of our results.