The emergence of large language models (LLMs) has provided robust support for application tasks across various domains, such as name entity recognition (NER) in the general domain. However, due to the particularity of the medical domain, the research on understanding and improving the effectiveness of LLMs on biomedical named entity recognition (BNER) tasks remains relatively limited, especially in the context of Chinese text. In this study, we extensively evaluate several typical LLMs, including ChatGLM2-6B, GLM-130B, GPT-3.5, and GPT-4, on the Chinese BNER task by leveraging a real-world Chinese electronic medical record (EMR) dataset and a public dataset. The experimental results demonstrate the promising yet limited performance of LLMs with zero-shot and few-shot prompt designs for Chinese BNER tasks. More importantly, instruction fine-tuning significantly enhances the performance of LLMs. The fine-tuned offline ChatGLM2-6B surpassed the performance of the task-specific model BiLSTM+CRF (BC) on the real-world dataset. The best fine-tuned model, GPT-3.5, outperforms all other LLMs on the publicly available CCKS2017 dataset, even surpassing half of the baselines; however, it still remains challenging for it to surpass the state-of-the-art task-specific models, i.e., Dictionary-guided Attention Network (DGAN). To our knowledge, this study is the first attempt to evaluate the performance of LLMs on Chinese BNER tasks, which emphasizes the prospective and transformative implications of utilizing LLMs on Chinese BNER tasks. Furthermore, we summarize our findings into a set of actionable guidelines for future researchers on how to effectively leverage LLMs to become experts in specific tasks.