Document-level event factuality identification is an important subtask in event factuality and is crucial for discourse understanding in Natural Language Processing (NLP). Previous studies mainly suffer from the scarcity of suitable corpus and effective methods. To solve these two issues, we first construct a corpus annotated with both document- and sentence-level event factuality information on both English and Chinese texts. Then we present an LSTM neural network based on adversarial training with both intra- and inter-sequence attentions to identify document-level event factuality. Experimental results show that our neural network model can outperform various baselines on the constructed corpus.