In this work, we take the named entity recognition task in the English language as a case study and explore style transfer as a data augmentation method to increase the size and diversity of training data in low-resource scenarios. We propose a new method to effectively transform the text from a high-resource domain to a low-resource domain by changing its style-related attributes to generate synthetic data for training. Moreover, we design a constrained decoding algorithm along with a set of key ingredients for data selection to guarantee the generation of valid and coherent data. Experiments and analysis on five different domain pairs under different data regimes demonstrate that our approach can significantly improve results compared to current state-of-the-art data augmentation methods. Our approach is a practical solution to data scarcity, and we expect it to be applicable to other NLP tasks.