Integrative analysis of distributed biomedical data is essential for maximizing knowledge discovery, accelerating medical breakthroughs, and improving patient care through collaborative research and practices. However, it is challenging to share and aggregate biomedical data distributed among multiple institutions or computing resources due to various concerns including data privacy, security, and confidentiality. The federated Learning (FL) framework can effectively enable multiple institutions to jointly perform machine learning by training a robust model without sharing local data to satisfy the requirement of user privacy protection as well as data security. However, conventional FL methods are exposed to the risk of gradient leakage and cannot be directly applied to genomic data since they cannot address the unique challenges of data imbalance typically seen in biomedicine. To provide secure and efficient disease prediction based on biomedical data distributed across multiple parties, we propose an FL framework enhanced with differential privacy (FedDP) on trained model parameters. The key idea of FedDP is to deploy differential privacy on intermediate gradients that are computed and transmitted by optimizers from local parties. In addition, the unique weighted min-max loss in FedDP is deployed to address the challenge of fair prediction on highly imbalanced datasets. Our experiments on label-imbalanced datasets for cancer prediction demonstrate that FedDP provides a powerful tool to implement and evaluate various strategies in support of privacy preservation and model performance guarantee to overcome data imbalance.