Neural named entity recognition (NER) models may easily encounter the over-confidence issue, which degrades the performance and calibration. Inspired by label smoothing and driven by the ambiguity of boundary annotation in NER engineering, we propose boundary smoothing as a regularization technique for span-based neural NER models. It re-assigns entity probabilities from annotated spans to the surrounding ones. Built on a simple but strong baseline, our model achieves results better than or competitive with previous state-of-the-art systems on eight well-known NER benchmarks. Further empirical analysis suggests that boundary smoothing effectively mitigates over-confidence, improves model calibration, and brings flatter neural minima and more smoothed loss landscapes.