(1) Background: More coronavirus disease 2019 (COVID-19) vaccines are gradually being developed and marketed. Improving the vaccination intention will be the key to increasing the vaccination rate in the future; (2) Methods: A self-designed questionnaire was used to collect data on COVID-19 vaccination intentions, protection motivation and control variables. Pearson Chi-square test and multivariate ordered logistic regression models were specified to analyze the determinants of intention to receive COVID-19 vaccine; (3) Results: Although the vaccine was free, 17.75% of the 2377 respondents did not want, or were hesitant, to receive the COVID-19 vaccine. Respondents’ cognition of vaccine safety, external reward and response efficacy were positively related to COVID-19 vaccination intention, while age, income and response cost were negatively related to the intention to receive the COVID-19 vaccine. Professionals and people without medical insurance had the lowest intention to vaccinate; (4) Conclusions: The older aged, people without health insurance, those with higher incomes and professionals should be treated as the key intervention targets. Strengthening publicity and education about the safety and efficacy of COVID-19 vaccines, training vaccinated people and community leaders as propagandists for the vaccine, and improving the accessibility to the COVID-19 vaccine are recommended to improve COVID-19 vaccination intention.