Recent studies have discovered that large language models (LLM) may be ``fooled'' to output private information, including training data, system prompts, and personally identifiable information, under carefully crafted adversarial prompts. Existing red-teaming approaches for privacy leakage either rely on manual efforts or focus solely on system prompt extraction, making them ineffective for severe risks of training data leakage. We propose LeakAgent, a novel black-box red-teaming framework for LLM privacy leakage. Our framework trains an open-source LLM through reinforcement learning as the attack agent to generate adversarial prompts for both training data extraction and system prompt extraction. To achieve this, we propose a novel reward function to provide effective and fine-grained rewards and design novel mechanisms to balance exploration and exploitation during learning and enhance the diversity of adversarial prompts. Through extensive evaluations, we first show that LeakAgent significantly outperforms existing rule-based approaches in training data extraction and automated methods in system prompt leakage. We also demonstrate the effectiveness of LeakAgent in extracting system prompts from real-world applications in OpenAI's GPT Store. We further demonstrate LeakAgent's effectiveness in evading the existing guardrail defense and its helpfulness in enabling better safety alignment. Finally, we validate our customized designs through a detailed ablation study. We release our code here https://github.com/rucnyz/LeakAgent.