A session-based news recommender system recommends the next news to a user by modeling the potential interests embedded in a sequence of news read/clicked by her/him in a session. Generally, a user's interests are diverse, namely there are multiple interests corresponding to different types of news, e.g., news of distinct topics, within a session. However, most of existing methods typically overlook such important characteristic and thus fail to distinguish and model the potential multiple interests of a user, impeding accurate recommendation of the next piece of news. Therefore, this paper proposes multi-interest news sequence (MINS) model for news recommendation. In MINS, a news encoder based on self-attention is devised on learn an informative embedding for each piece of news, and then a novel parallel interest network is devised to extract the potential multiple interests embedded in the news sequence in preparation for the subsequent next-news recommendations. The experimental results on a real-world dataset demonstrate that our model can achieve better performance than the state-of-the-art compared models. Our source code is publicly available on GitHub.