Traffic prediction is crucial for intelligent transportation systems, assisting in making travel decisions, minimizing traffic congestion, and improving traffic operation efficiency. Although effective, existing centralized traffic prediction methods have privacy leakage risks. Federated learning-based traffic prediction methods keep raw data local and train the global model in a distributed way, thus preserving data privacy. Nevertheless, the spatial correlations between local clients will be broken as data exchange between local clients is not allowed in federated learning, leading to missing spatial information and inferior prediction accuracy. To this end, we propose a federated graph neural network with spatial information completion (FedGCN) for privacy-preserving traffic prediction by adopting a federated learning scheme to protect confidentiality and presenting a mending graph convolutional neural network to mend the missing spatial information during capturing spatial dependency to improve prediction accuracy. To complete the missing spatial information efficiently and capture the client-specific spatial pattern, we design a personalized training scheme for the mending graph neural network, reducing communication overhead. The experiments on four public traffic datasets demonstrate that the proposed model outperforms the best baseline with a ratio of 3.82%, 1.82%, 2.13%, and 1.49% in terms of absolute mean error while preserving privacy.