Predicting future events in dynamic knowledge graphs has attracted significant attention. Existing work models the historical information in a holistic way, which achieves satisfactory performance. However, in real-world scenarios, the influence of historical information on future events is changing over time. Therefore, it is difficult to distinguish the historical information of different roles by invariably embedding historical entities with simple vector stacking. Furthermore, it is laborious to explicitly learn a distributed representation of each historical repetitive fact at different timestamps. This poses a challenge to the widely adopted codec-based architectures. In this paper, we propose a novel model for predicting future events, namely Distributed Attention Network (DA-Net). Rather than obtaining the fixed representations of historical events, DA-Net attempts to learn the distributed attention of future events on repetitive facts at different historical timestamps inspired by human cognitive theory. In human cognitive theory, when humans make a decision, similar historical events are replayed during memory recall. Based on memory, the original intention is adjusted according to their recent knowledge developments, making the action more reasonable to the context. Experiments on four benchmark datasets demonstrate a substantial improvement of DA-Net on multiple evaluation metrics.