Topic evolution is an important research task for Topic Detection and Tracking (TDT), studying how the topics evolve over time on textual data. On the web forum, topics are often interactive, which means that new topics emerge and old ones decay and the number of topics is always in a dynamic change. This paper presents an on-line adaptive topic evolution model based on Latent Dirichlet Allocation (LDA). This model uses the posterior of topics and word distribution in historical time window to adjust the prior of current by linear weighted, which is able to find the new topics and the vanished ones in text streams and automatically update the topic number. The experiment shows that the proposed model can identify the topic changes in terms of number well, and analyze their evolution in time and content; hence the hot spots can be discovered in time.