With the emergence and accumulation of massive data, data governance has become an important manner to improve data quality and maximize data value. Error detection is crucial for improving data quality, which has attracted a surge of interests from both industry and academia. Various detection methods tailored for a single data source have been proposed. Nevertheless, in many real-world scenarios, data is not centrally stored and managed. Different sources of correlated data can be employed to improve the accuracy of error detection. Unfortunately, due to privacy/security issues, cross-source data is often not allowed to be integrated centrally. To this end, this study proposes FeLeDetect, a cross-source data error detection method based on federated learning. First, a graph-based error detection model (GEDM) is presented to capture sufficient data features from each data source. Then, the study investigates a federated co-training algorithm (FCTA) to collaboratively train GEDM over different data sources without privacy leakage. Furthermore, the study designs a series of optimization methods to reduce the communication cost during the federated learning and the manual labeling efforts. Extensive experiments on three real-life datasets demonstrate that GEDM achieves an average improvement of 10.3% F1-score in the local scenario and 25.2% F1-score in the centralized scenario, outperforming all the five existing state-of-the-art competitors for a single data source; and FeLeDetect further enhances local GEDM in terms of F1-score by 23.2% on average.