Named entity recognition (NER) is a well-studied task in natural language processing. However, the widely-used sequence labeling framework is usually difficult to detect entities with nested structures. The span-based method that can easily detect nested entities in different subsequences is naturally suitable for the nested NER problem. However, previous span-based methods have two main issues. First, classifying all subsequences is computationally expensive and very inefficient at inference. Second, the span-based methods mainly focus on learning span representations but lack of explicit boundary supervision. To tackle the above two issues, we propose a boundary enhanced neural span classification model. In addition to classifying the span, we propose incorporating an additional boundary detection task to predict those words that are boundaries of entities. The two tasks are jointly trained under a multitask learning framework, which enhances the span representation with additional boundary supervision. In addition, the boundary detection model has the ability to generate high-quality candidate spans, which greatly reduces the time complexity during inference. Experiments show that our approach outperforms all existing methods and achieves 85.3, 83.9, and 78.3 scores in terms of F1 on the ACE2004, ACE2005, and GENIA datasets, respectively.