Information of internet public opinion is influenced by many netizens and net medias; characteristics of this information are non regular, stochastic, and may be expressed by a nonlinear complex evolution system. Corresponding model is difficult to establish and effectively predicted using the traditional methods based on statistical and machine learning. Characteristics of internet public opinion are chaotic, so the chaos theory can be introduced to research first, then the information of internet public opinion having chaotic characteristic is proved by the Lyapunov index. The model to predict the development trend of internet public opinion is next established by the phase space reconstruction theory. Finally, the hybrid algorithm EMPSO-RBF which is based on EM algorithm and the RBF neural network optimized by the improved PSO algorithm is proposed to solve the model. The hybrid algorithm fully takes the advantage of the EM clustering algorithm and the improved PSO, so the RBF neural network is improved by initializing the network structure in the early stage and optimizing the network parameters later. First, the EM clustering algorithm is used to obtain the center value and variance, and the radial basis function is improved with the combination of traditional Gauss model. Then the relevant network parameters are obtained by the improved PSO algorithm which is based on error optimizing the network parameters constantly. The model algorithm can be accurately simulated in the time series of chaotic information by experiments which are validated by different chaotic time series information; and it can better describe the development trend of different information of internet public opinion. The predicted results are made for government to monitor and guide the information of internet public opinion and benefit the social harmony and stability.