Medical large language models (LLMs) have gained popularity recently due to their significant practical utility. However, most existing research focuses on general medicine, and there is a need for in-depth study of LLMs in specific fields like anesthesiology. To fill the gap, we introduce Hypnos, a Chinese Anesthesia model built upon existing LLMs, e.g., Llama. Hypnos' contributions have three aspects: 1) The data, such as utilizing Self-Instruct, acquired from current LLMs likely includes inaccuracies. Hypnos implements a cross-filtering strategy to improve the data quality. This strategy involves using one LLM to assess the quality of the generated data from another LLM and filtering out the data with low quality. 2) Hypnos employs a general-to-specific training strategy that starts by fine-tuning LLMs using the general medicine data and subsequently improving the fine-tuned LLMs using data specifically from Anesthesiology. The general medical data supplement the medical expertise in Anesthesiology and enhance the effectiveness of Hypnos' generation. 3) We introduce a standardized benchmark for evaluating medical LLM in Anesthesiology. Our benchmark includes both publicly available instances from the Internet and privately obtained cases from the Hospital. Hypnos outperforms other medical LLMs in anesthesiology in metrics, GPT-4, and human evaluation on the benchmark dataset.