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In the age of Internet, people are using the social network services (SNS) to share information more frequently. Rumor spreading as a basic mechanism for information in online social network (OSN) has a significant impact on people's life. In this paper, A spreading model of rumor and derive differential equations that describe the dynamics of the model on online social network are introduced. Comparing with the Susceptible -Infected-Removed (SIR) model, we provide a more detailed and realistic description of rumor spreading process. Here we also study the rumor spreading model on an online social platform called Renren. Results show that the structure of network has an impact of rumor spreading, especially the role of community and bridge nod which neglected by previous studies in this field. Analysis results have revealed the characteristic of rumor, providing a valuable perspective for theoretical and practical aspects.