Personalized news recommendation is important for online news services. Many news recommendation methods recommend news based on their relevance to users' historical browsed news, and the recommended news usually have similar sentiment with browsed news. However, if browsed news is dominated by certain kinds of sentiment, the model may intensively recommend news with the same sentiment orientation, making it difficult for users to receive diverse opinions and news events. In this paper, we propose a sentiment diversity-aware neural news recommendation approach, which can recommend news with more diverse sentiment. In our approach, we propose a sentiment-aware news encoder, which is jointly trained with an auxiliary sentiment prediction task, to learn sentiment-aware news representations. We learn user representations from browsed news representations, and compute click scores based on user and candidate news representations. In addition, we propose a sentiment diversity regularization method to penalize the model by combining the overall sentiment orientation of browsed news as well as the click and sentiment scores of candidate news. Extensive experiments on real-world dataset show that our approach can effectively improve the sentiment diversity in news recommendation without performance sacrifice.