In medical information extraction, medical Named Entity Recognition (NER) is indispensable, playing a crucial role in developing medical knowledge graphs, enhancing medical question-answering systems, and analyzing electronic medical records. The challenge in medical NER arises from the complex nested structures and sophisticated medical terminologies, distinguishing it from its counterparts in traditional domains. In response to these complexities, we propose a medical NER model based on Machine Reading Comprehension (MRC), which uses a task-adaptive pre-training strategy to improve the model's capability in the medical field. Meanwhile, our model introduces multiple word-pair embeddings and multi-granularity dilated convolution to enhance the model's representation ability and uses a combined predictor of Biaffine and MLP to improve the model's recognition performance. Experimental evaluations conducted on the CMeEE, a benchmark for Chinese nested medical NER, demonstrate that our proposed model outperforms the compared state-of-the-art (SOTA) models.