Ever-growing electronic medical corpora provide unprecedented opportunities for researchers to analyze patient conditions and drug effects. Meanwhile, severe challenges emerged in the large-scale electronic medical records process phase. Primarily, emerging words for medical terms, including informal descriptions, are difficult to recognize. Moreover, although deep models can help in entity extraction on medical texts, they require large-scale labels, which are time-intensive to obtain and not always available in the medical domain. However, when encountering a situation where massive unseen concepts appear or labeled data is insufficient, the performance of existing algorithms will suffer an intolerable decline. In this article, we propose a balanced and deep active learning framework for Medical Named Entity Recognition (MedNER) to alleviate the above problems. Specifically, to describe our selection strategy precisely, we first define the uncertainty of a medical sentence as a labeling loss predicted by a loss-prediction module and define diversity as the least text distance between pairs of sentences in a sample batch computed based on word-morpheme embeddings. Furthermore, aiming to make a trade-off between uncertainty and diversity, we formulate a Distinct-K optimization problem to maximize the slightest uncertainty and diversity of chosen sentences. Finally, we propose a threshold-based approximation selection algorithm, Distinct-K Filter, which selects the most beneficial training samples by balancing diversity and uncertainty. Extensive experimental results on real datasets demonstrate that MedNER significantly outperforms existing approaches. CCS Concepts: center dot Computing methodologies -> Information extraction; Additional Key Words and Phrases: Named Entity Recognition; Active Learning; Medical Text Mining