Large Language Models (LLMs), despite their great power in language generation, often encounter challenges when dealing with intricate and knowledge-demanding queries in specific domains. This paper introduces a novel approach to enhance LLMs by effectively extracting the relevant knowledge from domain-specific textual sources, and the adaptive training of a chatbot with domain-specific inquiries. Our two-step approach starts from training a knowledge miner, namely LLMiner, which autonomously extracts Question-Answer pairs from relevant documents through a chain-of-thought reasoning process. Subsequently, we blend the mined QA pairs with a conversational dataset to fine-tune the LLM as a chatbot, thereby enriching its domain-specific expertise and conversational capabilities. We also developed a new evaluation benchmark which comprises four domain-specific text corpora and associated human-crafted QA pairs for testing. Our model shows remarkable performance improvement over generally aligned LLM and surpasses domain-adapted models directly fine-tuned on domain corpus. In particular, LLMiner achieves this with minimal human intervention, requiring only 600 seed instances, thereby providing a pathway towards self-improvement of LLMs through model-synthesized training data.