In this paper, an attack-defense framework is proposed for the remote H ∞ state estimation of delayed recurrent neural networks (RNNs). Firstly, an important-data-based (IDB) attack strategy is constructed, which can identify the important packets that play essential roles in the estimation and selectively attack them based on their importance degree from the perspective of the attackers. By targeting the important packets, larger attack damages can be achieved. Then, a resilient state estimator that can resist IDB attacks is developed from the defenders' point of view. Notably, some unrealistic assumptions (e.g., the attacker knowing the system structure and full parameters, the defender knowing the attack rate/parameters) are removed, which makes the proposed method easy to implement. At last, simulation results are presented to show the larger destructive effect of the constructed IDB attack and the efficiency of the proposed resilient H ∞ state estimator .