Understanding information propagation in online social networks is important in many practical applications and is of great interest to many researchers. The challenge with the existing propagation models lies in the requirement of complete network structure, topic-dependent model parameters and topic isolated spread assumption, etc. In this paper, we study the characteristics of multi-topic information propagation based on the data collected from Sina Weibo, one of the most popular microblogging services in China. We find that the daily total amount of user resources is finite and users’ attention transfers from one topic to another. This shows evidence on the competitions between multiple dynamical topics. According to these empirical observations, we develop a competition-based multi-topic information propagation model without social network structure. This model is built based on general mechanisms of resource competitions, i.e. attracting and distracting users’ attention, and considers the interactions of multiple topics. Simulation results show that the model can effectively produce topics with temporal popularity similar to the real data. The impact of model parameters is also analysed. It is found that topic arrival rate reflects the strength of competitions, and topic fitness is significant in modelling the small scale topic propagation.