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New vaccines are being developed in response to the coronavirus disease 2019 (COVID-19) pandemic. Vaccination provides a crucial preventive approach for managing COVID-19. We investigated adults’ willingness to take COVID-19 vaccines in the Zhejiang province, and their cognitions regarding COVID-19, when the COVID-19 vaccine is authorized under Emergency Use Administration. An online survey was conducted from September to October 2020, which included social-demographic characteristics, risk perception, acceptance and influencing factors in relation to COVID-19 vaccines. Multivariate logistic regression was performed to identify the influencing factors of vaccination acceptance. Of the participants, 70% intended to be vaccinated when the COVID-19 vaccine was approved under Emergency Use Administration, among 2171 valid questionnaires. Logistic regression revealed that being male, having a high cognitive score regarding COVID-19, the belief that the COVID-19 vaccine is safe and effective, and the belief that one will be infected with SARS-CoV-2 this fall and winter, were associated with a greater probability of accepting vaccination. Respondents with junior college/university education or above were less likely to accept vaccination. Concerns about the safety and effectiveness of the vaccine were the main factors hindering vaccination acceptance. Health education is important for promoting accurate public knowledge regarding COVID-19 vaccination.