Since the end of 2019, the ongoing of COVID-19 outbreak worldwide not only challenges the management capacity of governments on the public health emergency, but also tests the management capacity of governments on the public opinion and the governance capacity of dealing with social emergencies. To understand the impact on public emotion over COVID-19 related tweets posted by the major public health agency in the United States, this paper study the process and characteristics of public emotional diffusion in the tweets network by taking the four-official Twitter users of the public health system in the United States as an example. In this paper, we extract the interactions between tweets in the COVID-19-TweetIds dataset, draw the tweets diffusion network, propose a method to measure the characteristics of the emotional diffusion network, analyze the changes of the public emotional intensity and the proportion of emotional polarity, investigate the emotional influence of key nodes and users in the process of tweet emotional diffusion, and study the emotional diffusion of tweets of different tweeting time periods, topics and institutions. The results show that the emotional polarity of tweets has changed from negative to positive with the improvement of pandemic management measures. The public's emotional polarity on pandemic related topics tends to be negative, and the emotional intensity of management measures such as pandemic medical services turn from positive to negative to the greatest extent, while the emotional intensity of pandemic related knowledge changes the most. The tweets posted by the Centers for Disease Control and Prevention and the Food and Drug Administration of the United States have a broad impact on public emotions, and the emotional spread of tweets' polarity eventually forms a very close proportion of opposite emotions.