Most existing event extraction (EE) methods merely extract event arguments within the sentence scope. However, such sentence-level EE methods struggle to handle soaring amounts of documents from emerging applications, such as finance, legislation, health, etc., where event arguments always scatter across different sentences, and even multiple such event mentions frequently co-exist in the same document. To address these challenges, we propose a novel end-to-end model, Doc2EDAG, which can generate an entity-based directed acyclic graph to fulfill the document-level EE (DEE) effectively. Moreover, we reformalize a DEE task with the no-trigger-words design to ease the document-level event labeling. To demonstrate the effectiveness of Doc2EDAG, we build a large-scale real-world dataset consisting of Chinese financial announcements with the challenges mentioned above. Extensive experiments with comprehensive analyses illustrate the superiority of Doc2EDAG over state-of-the-art methods. Data and codes can be found at https://github.com/dolphin-zs/Doc2EDAG.