Background: Older individuals have a high risk of morbidity and mortality due to COVID-19, and one of the most effective ways to prevent COVID-19 is vaccination. Little is known about older people’s willingness to receive a COVID-19 vaccine. Therefore, the objective of this study was to assess the acceptance of and factors influencing the intention to receive a COVID-19 vaccination among older adults in Shanghai, China. Methods: A cross-sectional study was conducted among older adults (≥60 years old) in Shanghai. Face-to-face interviews with a questionnaire were conducted in community health service centers, recording several parameters: demographic information, health-related factors; perceived likelihood, severity, and burden of COVID-19; perceived safety, effectiveness, necessity, and benefit of the COVID-19 vaccine, as well as their trust in the vaccine delivery system and doctors; willingness to receive a COVID-19 vaccination. Bivariate analysis between several survey items and the willingness to receive a COVID-19 vaccination was conducted using a chi-square test. Logistic regression was used to assess to what degree each variable affected the willingness to receive a COVID-19 vaccination. Results: Of the 1067 participants, 90.91% (970/1067) confirmed that they were willing to receive a COVID-19 vaccination. The participants were more likely to be willing to be vaccinated if they were immigrants (OR = 1.988, 95%CI = 1.062–3.717), had an education level of junior high school (OR = 2.724, 95%CI = 1.000–7.423) or high school or above (OR = 3.993, 95%CI = 1.576–10.119), and had a monthly income of CNY 3000–5000 (OR = 32.770, 95%CI = 1.144–6.711) or CNY >5000 (OR = 2.309, 95%CI = 1.003–5.319). The participants were also more likely to be willing to be vaccinated if they had received a pneumonia vaccination previously (OR = 2.138, 95%CI = 1.016–4.500), perceived the safety of the COVID-19 vaccine (OR = 1.508, 95%CI = 1.073–2.119), perceived the necessity of the COVID-19 vaccine (OR = 2.604, 95%CI = 1.946–3.484), or trusted the suggestions of doctors (OR = 1.706, 95%CI = 1.115–2.618). The participants were less likely to be willing to be vaccinated if they were aged ≥76 years (OR = 0.498, 95%CI = 0.264–0.939), reported a physical health condition of bad or below (OR = 0.229, 95% CI = 0.095–0.549), or were worried about the adverse effects of a COVID-19 vaccination (OR = 0.503, 95%CI = 0.364–0.695). Conclusions: Under the free vaccination policy for COVID-19, older adults have a high intention to be vaccinated to prevent COVID-19 in Shanghai, China. Widely publicizing the safety and necessity of COVID-19 vaccination is necessary.