In the age of Web 2.0, modeling and predicting the popularity of online information was an important issue in information dissemination. Online social medium greatly affects the way we communicate with each other. However, little is known about what fundamental mechanisms drive the dynamical information flow in online social systems. To address this problem, we develop a theoretical probabilistic model based on branching process to characterize the process in which micro-blog information gains its popularity. Firstly, the data of information popularity and network structure of micro-blog network are analyzed. The statistical results show that the attenuation of information popularity follows a scaling law whose exponent is 1.8, and in-degree and out-degree of micro-blog network each also obey a power law distribution whose exponent is 1.5. The results of power law distribution show that there is a high-degree heterogeneity in a micro-blog system. The proportion of micro-blog information with popularity less than 100 is 95.8%, while the amount of micro-blog information with popularity more than 10, 000 is very small. The number of fans (in-degree) less than 100 accounts for 56.4%, while some users have millions of fans.Secondly, according to the design mechanism of the Weibo system, we assume that each user has two lists, i.e. a "home page list" and a "personal page list". Meanwhile, each user has two states at each moment: generating a new message with probability ${\mu} $ to be sent out; 2) or forwarding the information already on the "personal page list" with probability $ (1-{\mu}) $ . Based on the assumptions, the information popularity model is proposed. Finally, the model is simulated. The simulation results show that the model can reproduce some features of real social network data, and the popularity of information is related to the network structure. By solving the model equation, the results of theoretical prediction are consistent with the simulation analyses and actual data.