Named entity recognition (NER) is a fundamental problem in natural language processing. In particular, nested entities are commonly existed in real-life textual data for the NER task. However, the current span-based methods for nested NER are computationally expensive, lacking of explicit boundary supervision and generating many negative samples for span classification, which affect their overall performance. In this paper, we propose a Segment Enhanced Span-based model for nested NER (SESNER). The proposed model treats the nested NER task as a segment covering problem. First, it models entities as segments, detects the segment endpoints and identifies the positional relationship between neighboring endpoints. Then, it detects the outermost segments to generate candidate entity spans nested in it for span classification. Our proposed model has the advantages of enhancing boundary supervision in learning span representations by detecting segment endpoints, reducing the number of negative samples without losing long entities that are ignored by most span-based methods, and improving runtime performance. Moreover, a novel augmented training mechanism is also proposed to further improve the model performance by extending the training dataset with data that were wrongly predicted before. Experimental results show that our proposed SESNER model has achieved promising performance with near linear time complexity on the benchmark datasets.