<p>This paper investigates the exponential synchronization problem of complex dynamical networks (CDNs) with time-varying delays under deception attacks by applying the Lyapunov-based event-triggered delayed impulsive control (ETDIC) strategy. Considering that the density of triggering signals in the event-triggering mechanism drops significantly when the network approaches the optimal state, the forced impulsive sequence is introduced in this paper to ensure the stability and rapidity of the network convergence. Building upon this framework, the definition of average delayed impulsive gains (ADIG) is proposed, which assesses the impacts on the network from the perspective of the cumulative effects of impulsive delays and impulsive gains over time. On this basis, the traditional comparison principle is elaborately extended to the case with hybrid delayed impulses. By means of the formula for the variation of parameters, sufficient conditions for achieving the exponential synchronization of the networks are eventually obtained, and meanwhile, the Zeno behavior is successfully eliminated. Finally, numerical simulations validate the theoretical findings and demonstrate the proposed methodology’s efficacy.</p>