It is helpful for institutions to master the whole trends of target group that research on keywords popularity of network public opinions from a macroscopic perspective, precisely formulating corresponding strategies to enhance the level of opinion guidance. With Sina Weibo data set as an example, Factor Analysis (FA) is used to mine the internal factors of public opinions; a model that analyzes and predicts the keyword popularity of network public opinions is created through the initial parameters optimized by Genetic Algorithm (GA) and Elman network structure. The results show that predictions made by our method is more precise than those of original data sets and standard Elman network. Thus, it can be applied to providing reference for decision making.