Background Psychological resilience may reduce the impact of psychological distress to some extent. We aimed to investigate the mental health status of the public during the outbreak of coronavirus disease 2019 (COVID-19) and explore the level and related factors of anxiety and depression. Methods From February 8 to March 9, 2020, 3,180 public completed the Zung's Self-Rating Anxiety Scale (SAS) for anxiety, Zung's Self-Rating Depression Scale (SDS) for depression, the Connor-Davidson resilience scale (CD-RISC) for psychological resilience, and the Simplified Coping Style Questionnaire (SCSQ) for the attitudes and coping styles. Results The number of people with depressive symptoms (SDS > 53) was 1,303 (the rate was 41.0%). The number of people with anxiety symptoms (SAS > 50) was 1,184 (the rate was 37.2%). The depressed group and anxiety group had less education, more unmarried and younger age, as well as had significant different in SDS total score (P < 0.001), SAS total score (P < 0.001), CD-RISC total score (P < 0.001), and SCSQ score (P < 0.001). The binary logistic regression showed that female (B = -0.261, P = 0.026), strength (B = -0.079, P = 0.000), and the subscales of active coping style in SCSQ (B = -0.983, P = 0.000) remained protective factors and passive coping style (B = 0.293, P = 0.003) and higher SAS score (B = 0.175, P = 0.000) were risk factors for depression. Optimism (B = -0.041, P = 0.015) in CD-RISC was a protective factor, and passive coping styles (B = 0.483, P = 0.000) and higher SDS score (B = 0.134, P = 0.000) were risk factors for anxiety. Limitations This study adopted a cross-sectional design and used self-report questionnaires. Conclusion The mental health of the public, especially females, the younger and less educational populations, and unmarried individuals, should be given more attention. Individuals with high level of mental resilience and active coping styles would have lower levels of anxiety and depression during the outbreak of COVID-19.