Millions of patients suffer from rare diseases around the world. However, the samples of rare diseases are much smaller than those of common diseases. In addition, due to the sensitivity of medical data, hospitals are usually reluctant to share patient information for data fusion citing privacy concerns. These challenges make it difficult for traditional AI models to extract rare disease features for the purpose of disease prediction. In this paper, we overcome this limitation by proposing a novel approach for rare disease prediction based on federated meta-learning. To improve the prediction accuracy of rare diseases, we design an attention-based meta-learning (ATML) approach which dynamically adjusts the attention to different tasks according to the measured training effect of base learners. Additionally, a dynamic-weight based fusion strategy is proposed to further improve the accuracy of federated learning, which dynamically selects clients based on the accuracy of each local model. Experiments show that with as few as five shots, our approach out-performs the original federated meta-learning algorithm in accuracy and speed. Compared with each hospital's local model, the proposed model's average prediction accuracy increased by 13.28%.