Retrieval-Augmented Generation (RAG) has recently emerged as a promising solution for enhancing the accuracy and credibility of Large Language Models (LLMs), particularly in Question & Answer tasks. This is achieved by incorporating proprietary and private data from integrated databases. However, private RAG systems face significant challenges due to the scarcity of private domain data and critical data privacy issues. These obstacles impede the deployment of private RAG systems, as developing privacy-preserving RAG systems requires a delicate balance between data security and data availability. To address these challenges, we regard federated learning (FL) as a highly promising technology for privacy-preserving RAG services. We propose a novel framework called Federated Retrieval-Augmented Generation (FedE4RAG). This framework facilitates collaborative training of client-side RAG retrieval models. The parameters of these models are aggregated and distributed on a central-server, ensuring data privacy without direct sharing of raw data. In FedE4RAG, knowledge distillation is employed for communication between the server and client models. This technique improves the generalization of local RAG retrievers during the federated learning process. Additionally, we apply homomorphic encryption within federated learning to safeguard model parameters and mitigate concerns related to data leakage. Extensive experiments conducted on the real-world dataset have validated the effectiveness of FedE4RAG. The results demonstrate that our proposed framework can markedly enhance the performance of private RAG systems while maintaining robust data privacy protection.