Rumor is a kind of information to be confirmed. Before the rumor is falsified, the research on the interaction and confrontation between online rumor with different authenticity grade and the positive information can provide scientific basis for efficient and low-cost rumor refutation. Analyze the mechanism of the occurrence of online rumors in public crisis, improve the rumor spreading formula by proposing the rumor authenticity parameter, build a macro model of online rumor spreading based on the change of the number of news posts of Baidu, and carry out simulation analysis and empirical test. The results show that rumors with high authenticity grade spread wider and need positive information with more persuasive and emotional guidance to contain. Therefore, rumors should be refuted hierarchically according to their authenticity grade so as to save administrative costs and scotch them accurately.