The COVID-19 pandemic has created a global health crisis that has affected economies and societies worldwide. During these times of uncertainty and crisis, people have turned to social media platforms as communication tools and primary information sources. Online discourse is conducted under the influence of many different factors, such as background, culture, politics, etc. However, parallel comparative research studies conducted in different countries to identify similarities and differences in online discourse are still scarce. In this study, we combine the crisis lifecycle and opinion leader concepts and use data mining and a set of predefined search terms (coronavirus and COVID-19) to investigate discourse on Twitter (101,271 tweets) and Sina Weibo (92,037 posts). Then, we use a topic modeling technique, Latent Dirichlet Allocation (LDA), to identify the most common issues posted by users and temporal analysis to research the issue’s trend. Social Network Analysis (SNA) allows us to discover the opinion leader on the two different platforms. Finally, we find that online discourse reflects the crisis lifecycle according to the stage of COVID-19 in China and the US. Regarding the status of the COVID-19 pandemic, users of Twitter tend to pay more attention to the economic situation while users of Weibo pay more attention to public health. The issues focused on in online discourse have a strong relationship with the development of the crisis in different countries. Additionally, on the Twitter platform many political actors act as opinion leaders, while on the Weibo platform official media and government accounts control the release of information.