<p>In this paper, the issue of exponential synchronization in chaotic neural networks with system time-varying delay is investigated by employing delayed impulsive control. In order to tackle the challenge posed by the flexible delay existing in impulsive controller, the concept of average impulsive delay (AID) is adopted, which considers time delay in impulse from a holistic perspective. Then, some Lyapunov-based relaxed synchronization conditions are established by applying average impulsive interval and AID methods, where such delay is no longer constrained by some strong conditions. Meanwhile, considering different functionalities of impulsive signal, the convergence rates are precisely calculated, which indicates that the system delay may either promote or impede network synchronization. In addition, the results also clearly show that the time delay in impulse plays either a positive or a negative role in the synchronization of chaotic neural networks. Moreover, allow for the controller involving synchronizing and desynchronizing delayed impulses, the notion of average impulsive estimation serves to address time-varying impulsive effects. Ultimately, three examples are simulated to exemplify the rightness of the theoretical results.</p>