Topic-level social influence analysis has been playing an important role in the online social networks like microblogs. Previous works usually use the cumulative number of links, such as the number of followers, to measure users’ topic-level influence in a static network. However, they ignore the dynamics of influence and the methods they proposed can not be applied to social streams. To address the limitations of prior works, we firstly propose a novel topic-level influence over time (TIT) model integrating the text, links and time to analyze the topic-level temporal influence of each user. We then design an influence decay based approach to measure users’ topic-level influence from the learned temporal influence. In order to track the influencers in data streams, we combine TIT and the influence decay method into a united online model (named oTIT), which is applicable to dynamic scenario. Through extensive experiments, we demonstrate the superiority of our approach, compared with the baseline and the state-of-the-art method. Moreover, we discover influence exhibits significantly different variation patterns over different topics, which verifies our viewpoint and gives us a new angle to understand its dynamic nature.