Nowadays, people receive information of the news stories not only from newspapers but also from online news websites. They search important news stories in order to know what happen today. However, it is hard to browse all the news stories published on a day. It is necessary to identify which news stories are more newsworthy on the specific day. In this paper, we investigate how to automatically identify the importance of news stories for different news categories on a specific day by utilizing the influence propagation among communities and news categories. In particular, we build an influence propagation model which consists of three features: category relevance, bloggers' attention and bursty influence. Based on this influence propagation model, we propose a Cross-Category Social Influence Propagation (C-SIP) approach for scoring the importance of news stories on a specific day. We evaluate our approach by using the judgment of Story Ranking Task in TREC 2010 Blog Track. The experiment shows our approach attains a prominent performance in the retrieval of important news stories and gets 9.94% improvement over the best performance of participating systems in TREC 2010 Blog Track.