The COVID-19 epidemic has been confirmed as the largest scale outbreak of atypical pneumonia since the outbreak of severe acute respiratory syndrome (SARS) in 2003 and it has become a public health emergency of international concern. It exacerbated public confusion and anxiety, and the impact of COVID-19 on people needs to be better understood. Indeed, prior studies that conducted meta-analysis of longitudinal cohort research compared mental health before versus during the COVID-19 pandemic and proved that public health polices (e.g., city lockdowns, quarantines, avoiding gatherings, etc.) and COVID-19-related information that circulates on new media platforms directly affected citizen’s mental health and well-being. Hence, this research aims to explore Taiwanese people’s health status, anxiety, media sources for obtaining COVID-19 information, subjective well-being, and safety-seeking behavior during the COVID-19 epidemic and how they are associated. Online surveys were conducted through new media platforms, and 342 responses were included in the analysis. The research results indicate that the participants experienced different aspects of COVID-19 anxiety, including COVID-19 worry and perceived COVID-19 risk. Among the given media sources, the more participants searched for COVID-19 information on new media, the greater they worried about COVID-19. Furthermore, COVID-19 worry was positively related to safety-seeking behavior, while perceived COVID-19 risk was negatively related to subjective well-being. This paper concludes by offering some suggestions for future studies and pointing out limitations of the present study.