Background: To increase vaccination coverage, it is important to understand COVID-19 vaccination programs and respondents’ acceptance. Therefore, this study aimed to measure respondents’ knowledge of the COVID-19 vaccine and its acceptance among Indonesian adults in Java. Methods: A web-based survey was distributed through social media on self-claimed knowledge, risk and benefits of the vaccine, as well as respondents’ acceptance and experiences of the vaccination. The survey period was from March to July 2021, and 910 responses were included for further analysis. The frequency of each categorical factor, including self-claimed knowledge of the COVID-19 vaccine, their descriptive benefit and side effects of the COVID-19 vaccine, and their experiences receiving or not receiving the vaccine were explored. Predictor factors on vaccine knowledge and acceptance are investigated using multivariate ordinal regression analysis. Results: This study showed that almost all the respondents in both groups have knowledge about COVID-19 vaccination, or at least ever heard about it. The main source of information is social media. More than two third of respondents from each group had already received a COVID-19 vaccine or were at least on the waiting list. Moreover, a quarter of the respondents still hesitate to receive the vaccination. Only less than 10% of respondents reject the vaccination, with the strongest reason being scared of the side effect. Moreover, it found that respondents’ knowledge of the vaccination was influenced by age, medical background, a history of relatives who tested positive for COVID-19, source of information, economic status, and education levels. Moreover, the acceptance was influenced by age, knowledge about vaccines, and having medical background. Conclusions: This study showed high levels of knowledge and acceptance of the COVID-19 vaccine among adults in Java. Increasing understanding or knowledge about COVID-19 vaccine risks and benefits is necessary to reduce vaccination hesitancy.