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We tackle a new task, event graph completion, which aims to predict missing event nodes for event graphs. Existing link prediction or graph completion methods have difficulty dealing with event graphs because they are usually designed for a single large graph such as a social network or a knowledge graph, rather than multiple small dynamic event graphs. Moreover, they can only predict missing edges rather than missing nodes. In this work, we propose to utilize event schema, a template that describes the stereotypical structure of event graphs, to address the above issues. Our schema-guided event graph completion approach first maps an instance event graph to a subgraph of the schema graph by a heuristic subgraph matching algorithm. Then it predicts whether a candidate event node in the schema graph should be added to the instantiated schema subgraph by characterizing two types of local topology of the schema graph: neighbors of the candidate node and the subgraph, and paths that connect the candidate node and the subgraph. These two modules are later combined together for the final prediction. We also propose a self-supervised strategy to construct training samples, as well as an inference algorithm that is specifically designed to complete event graphs. Extensive experimental results on four datasets demonstrate that our proposed method achieves state-of-the-art performance, with 4.3% to 19.4% absolute F1 gains over the best baseline method on the four datasets.