Describing the behavior of information dissemination in online social networks is propitious to understanding the transmission process of real users in the online social networking site. In this paper, we proposed a cellular automaton model to deal with the propagation characteristics of online social networks rumors spread. Experimental simulation was carried out under periodic boundary constraints in the process of rumor spread. The result showed that the cellular automaton model is indeed able to characterize the propagation behavior on online social networks. We also prescribed the immunization strategy to suppress the rumor spreading.