Public health emergencies, especially major infectious diseases, may cause global crises. Timely and effective communication is essential for response to such incidents. However, the emergency response to such incidents usually lasts longer and break out repeatedly, and the existing static emergency communication network (ECN) analysis cannot fully reflect the dynamic information interaction between organizations during the emergency process. Therefore, this article takes the recent COVID-19 epidemic in Hubei, China as a case, and uses social network analysis to reveal the dynamic evolution of communication networks, positions, roles, and tasks of organizations from the time dimension. The results show that: (1) the ECN has changed from concentrated to decentralized over time; (2) the positions and roles of participating organizations in the ECN has changed, but there are still a few key organizations that at the central position in all phases of emergency communication; (3) the core tasks have changed due to emergency needs at each stage; (4) under the concentrated management system, the core organization of the ECN mainly comes from government organizations. The research results reveal the dynamic evolution of communication networks between different types of emergency organizations, which is beneficial to guide emergency management of public health emergencies. In actual emergency, the emergency communication mode should be dynamically adjusted based on the characteristics of the emergency situation at different stages, comprehensively using the advantages of the concentrated and decentralized emergency network. In addition, communication between different types of organizations such as governments, research institutions, and enterprises should be strengthened, and channels for diversified organizations to participate in emergency communication should be set up. The research helps to improve communication between emergency response organizations and is of great significance to controlling and reducing the harm caused by public health emergencies.