The span-based approach is highly efficient for handling Nested Named Entity Recognition (NNER). However, in previous studies, span representations were generated by integrating the endpoint word representations of the span or by integrating all the word representations within the span, without fully considering the local dependencies among different words within the span. Furthermore, when using feature matrices for entity prediction, the dependencies between entities and the contextual information of entities in a sentence were not considered. To address these issues, we propose a Span-Enhanced Network (SEnNet), which utilizes word pair information within the span to construct initial span representations. These span representations are then gradually enriched through interactions between different spans and the introduction of contextual information. Experimental results show that the proposed model achieves the best performance compared to 10 advanced baseline models on three nested datasets and one non-nested dataset. Further experimental analysis shows that fully leveraging word pair information within spans helps enhance the recognition performance of entities of different lengths, especially long entities.