For the problem of existing models' disability to analyze topic-sentiment evolution of microblogs, a Dynamic Topic Sentiment Combining Model (DTSCM) was proposed based on Topic Sentiment Combining Model (TSCM) and the emotional cycle theory. DTSCM could track the topic sentiment evolution trend and obtain the graph of topic sentiment evolution so as to analyze the evolution of topic and sentiment by capturing the topic and sentiment of microblogs in different time. The experimental results in real microblog corpus showed that, in contrast with state-of-the-art models Joint Sentiment/Topic (JST), Sentiment-Latent Dirichlet Allocation (S-LDA) and Dependency Phrases-Latent Dirichlet Allocation (DPLDA), the sentiment classification accuracy of DTSCM increased by 3.01%, 4.33% and 8.75% respectively,and DTSCM could obtain topic-sentiment evolution of microblogs. The proposed approach can not only achieve higher sentiment classification accuracy but also analyze topic-sentiment evolution of microblog, and it is helpful for public opinion analysis.