Millions of patients suffer from rare diseases around the world. However, the samples of rare diseases are much smaller than those of common diseases. Hospitals are usually reluctant to share patient information for data fusion due to the sensitivity of medical data. These challenges make it difficult for traditional AI models to extract rare disease features for disease prediction. In this paper, we propose a Dynamic Federated Meta-Learning (DFML) approach to improve rare disease prediction. We design an Inaccuracy-Focused Meta-Learning (IFML) approach that dynamically adjusts the attention to different tasks according to the accuracy of base learners. Additionally, a dynamic weight-based fusion strategy is proposed to further improve federated learning, which dynamically selects clients based on the accuracy of each local model. Experiments on two public datasets show that our approach outperforms the original federated meta-learning algorithm in accuracy and speed with as few as five shots. The average prediction accuracy of the proposed model is improved by 13.28% compared with each hospital's local model.