During the Omni-media era, the in-depth advancement of intelligent process endowed public opinion information (referred to as public opinion) with unique spreading characteristics, and put forward new and higher requirements for its governance. Against this background, we proposed an improved public opinion propagation model coupling the possible factors to grasp its spreading rules. Then, the spreading characteristics of public opinion and its governance timing-intensity-effect in online social networks (OSN) were discussed through numerical simulations. Our results showed that the propagation of public opinion shows faster speed and is more dependent on netizens' attributes in open OSN with a wider scope and depends more on information content in closed OSN. During the governance process of public opinion propagation, the regulators' strategies should have priority: Governance timing $\succ$ governance proportion $\succ$ punishment intensity. Based on research findings, targeted countermeasures and decision-making references were provided for the regulators to reasonably guide the evolution trend of public opinion.