Firstly, this paper establishes a cloud computing public opinion management business model based on distributed collection analysis, consultative decision and concurrent collaborative behavior. At the same time, this paper studies the public opinion management system from the logical framework, network structure and security index. Then this paper uses the weak correlation mining technology of probability theory statistics to establish a public health and safety public opinion prediction system composed of three dimensions. The content includes three levels of public opinion bonding, thermal and trend. Then, this paper forecasts the development of public opinion events by combining K-Means clustering and grey correlation degree. The results show that this method is suitable for public opinion prediction in public health and safety.