Artificial Intelligence (AI), along with the recent progress in biomedical language understanding, is gradually offering great promise for medical practice. With the development of biomedical language understanding benchmarks, AI applications are widely used in the medical field. However, most benchmarks are limited to English, which makes it challenging to replicate many of the successes in English for other languages. To facilitate research in this direction, we collect real-world biomedical data and present the first Chinese Biomedical Language Understanding Evaluation (CBLUE) benchmark: a collection of natural language understanding tasks including named entity recognition, information extraction, clinical diagnosis normalization, single-sentence/sentence-pair classification, and an associated online platform for model evaluation, comparison, and analysis. To establish evaluation on these tasks, we report empirical results with the current 11 pre-trained Chinese models, and experimental results show that state-of-the-art neural models perform by far worse than the human ceiling.