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In the period of Corona Virus Disease 2019 (COVID-19), millions of people participate in the discussion of COVID-19 on the Internet, which can easily trigger public opinion and threaten social stability. This paper creatively proposes a multi-stage risk grading model of Internet public opinion for public health emergencies. On the basis of general public opinion risk grading analysis, the model continuously pays attention to the risk level of Internet public opinion based on the time scale of regular or major information updates. This model combines Analytic Hierarchy Process Sort II (AHPSort II) and Swing Weighting (SW) methods and proposes a new Multi-Criteria Decision Making (MCDM) method – AHPSort II-SW. Intuitionistic fuzzy number and linguistic fuzzy number are introduced into the model to evaluate the criteria that cannot be quantified. The multi-stage model is tested using more than 2,000 textual data about COVID-19 collected from Microblog, a leading social media platform in China. Seven public opinion risk assessments were conducted from January 23 to April 8, 2020. The empirical results show that in the early COVID-19 outbreak, the risk of public opinion is more serious on macroscopic view. In details, the risk of public opinion decreases slowly with time, but the emergence of important events may still increase the risk of public opinion. The analysis results are in line with the actual situation and verify the effectiveness of the method. Comparative analysis indicates the improved method is proved to be superior and effective, sensitivity analysis confirms its stability. Finally, management suggestions was provided, this study contributes to the literature on public opinion risk assessment and provides implications for practice.