The progress of false information diffusion in the public crisis is harmful to the society. When the public crisis occurs, the public respond in different ways and the public also want to tell others what they think right. But what they think is right is not recognized by the government. Thus the false information forms and it begins to diffuse. As the false information spreads, the harm to society magnifies gradually. Particularly in network society, false information diffusion can easily cause secondary hazards and accelerate public crises to a devastating degree. Thus intervening and controlling the false information diffusion is an important aspect of the public crisis management. From the perspective of the social network theory, this study analyzes the progress of false information diffusion in terms of different public crisis management strategies and presents the result of false information diffusion through simulation on cellular automaton of different public crisis management strategies. In simulations on cellular automaton, interventions are also carried to control false information diffusion and alternatives are proposed to help reduce public crises. This study also extends the theory of false information management, which is significant for the government to improve the ability to evaluate the false information and carry out interventions effectively to control the false information when it begins to diffuse.