The recent coronavirus outbreak has captured worldwide attention. This study investigated the anxiety of the Chinese public and its relationship with social support during the early stage of the COVID-19 pandemic, thereby providing empirical support for interventions on improving the public’s mental health. On the basis of an online questionnaire survey conducted on 10–18 February 2020, this study shows that 19.8%, 68.5%, and 11.1% of the respondents suffered mild anxiety, moderate anxiety, and severe anxiety, respectively. Significant differences are reported in state anxiety between people with different household incomes. There are significant differences in trait anxiety and state anxiety between different social support groups. Social support and trait anxiety are negatively correlated. Social support and state anxiety are negatively correlated. Social support affects state anxiety both directly and indirectly (through the mediation of trait anxiety). Therefore, during the COVID-19 pandemic, increasing public support for society can effectively reduce public anxiety.