Abstract Background It is hypothesized that anxiety and behavioral responses are intense at the beginning of an epidemic. The objective of this study was to investigate anxiety symptoms and use of preventive measures against COVID-19. The study also compared the association between preventive measures and anxiety symptoms during the week immediately preceding the study and those symptoms and measures at the beginning of the outbreak. Methods A cross-sectional population survey using an online questionnaire commenced on 14 February 2020. The study participants were residents of Taiwan ages 20 to 70 years. The 6-item state version of the State–Trait Anxiety Inventory (STAI-6) was used to assess anxiety symptoms. The questions about preventive measures asked participants about their personal protection, cough etiquette, contact precautions, voluntary quarantine, and prompt reporting. Multivariable logistic regression was used to determine the factors influencing an increase in the preventive measures scores. Results Of a total of 3555 completed responses, a total of 52.1% (95% confidence interval [CI] 50.4–53.7) of the respondents reported moderate to severe levels of anxiety symptoms in the past week, whereas 48.8% (95%CI 47.2–50.5) reported moderate to severe anxiety symptoms at the beginning of the outbreak. With a higher score indicating greater anxiety, the median scores for anxiety symptoms in the past week and at the beginning of the outbreak were 46.7 (IQR [interquartile range] 36.7–53.3) and 43.3 (IQR 36.7–53.3), respectively. The median scores for the preventive measures taken in the past week and at the beginning of the outbreak were 26.0 (IQR 21.0–30.0) and 24.0 (IQR 19.0–28.0), respectively, out of a maximum score of 36. In the multivariable analysis, an increased anxiety symptom score from the beginning of the outbreak to the past week (adjusted OR = 7.38, 95%CI 6.28–8.66) was a strongly significant determinant of an increased preventive measures score in the past week compared with the score at the beginning of the outbreak. Conclusions Anxiety and preventive measures scores were high and increased with the epidemic rate. Higher anxiety was associated with an increased use of preventive measures against COVID-19.