Title: Federated causal discovery. Abstract: Causal discovery aims to learn a causal graph from observational data. To date, most causal discovery methods require data to be stored in a central server. However, data owners gradually refuse to share personalized data to avoid privacy leakage, making this task more troublesome by cutting off the first step. The puzzle, \textit{how do we infer causal relations from decentralized data?} arises. In this paper, we take a first step in developing a gradient-based learning framework named DAG-Shared Federated Causal Discovery (DS-FCD), which can learn the causal graph without directly touching local data and naturally handle the data heterogeneity. DS-FCD benefits from a two-level structure of each local model. The first level learns the causal graph and communicates with the server to get training information from other clients, while the second level approximates causal mechanisms and personally updates from its own data to accommodate the data heterogeneity. Moreover, DS-FCD formulates the overall learning task as a continuous optimization problem by taking advantage of an equality acyclicity constraint, which can be naturally solved by gradient descent methods. Extensive experiments on both synthetic and real-world data sets verify the efficacy of the proposed method.