The success of large language models (LLMs) facilitate many parties to fine-tune LLMs on their own private data. However, this practice raises privacy concerns due to the memorization of LLMs. Existing solutions, such as utilizing synthetic data for substitution, struggle to simultaneously improve performance and preserve privacy. They either rely on a local model for generation, resulting in a performance decline, or take advantage of APIs, directly exposing the data to API servers. To address this issue, we propose KnowledgeSG, a novel client-server framework which enhances synthetic data quality and improves model performance while ensuring privacy. We achieve this by learning local knowledge from the private data with differential privacy (DP) and distilling professional knowledge from the server. Additionally, inspired by federated learning, we transmit models rather than data between the client and server to prevent privacy leakage. Extensive experiments in medical and financial domains demonstrate the effectiveness of KnowledgeSG. Our code is now publicly available at https://github.com/wwh0411/KnowledgeSG.