Bangladesh govt. launched a nationwide vaccination drive against SARS-CoV-2 infection from early February 2021. The objectives of this study were to evaluate the acceptance of the COVID-19 vaccines and examine the factors associated with the acceptance in Bangladesh. In between January 30 to February 6, 2021, we conducted a web-based anonymous cross-sectional survey among the Bangladeshi general population. At the start of the survey, there was a detailed consent section that explained the study's intent, the types of questions we would ask, the anonymity of the study, and the study's voluntary nature. The survey only continued when a respondent consented, and the answers were provided by the respondents themselves. The multivariate logistic regression was used to identify the factors that influence the acceptance of the COVID-19 vaccination. A total of 605 eligible respondents took part in this survey (population size 1630046161 and required sample size 591) with an age range of 18 to 100. A large proportion of the respondents are aged less than 50 (82%) and male (62.15%). The majority of the respondents live in urban areas (60.83%). A total of 61.16% (370/605) of the respondents were willing to accept/take the COVID-19 vaccine. Among the accepted group, only 35.14% showed the willingness to take the COVID-19 vaccine immediately, while 64.86% would delay the vaccination until they are confirmed about the vaccine's efficacy and safety or COVID-19 becomes deadlier in Bangladesh. The regression results showed age, gender, location (urban/rural), level of education, income, perceived risk of being infected with COVID-19 in the future, perceived severity of infection, having previous vaccination experience after age 18, having higher knowledge about COVID-19 and vaccination were significantly associated with the acceptance of COVID-19 vaccines. The research reported a high prevalence of COVID-19 vaccine refusal and hesitancy in Bangladesh. To diminish the vaccine hesitancy and increase the uptake, the policymakers need to design a well-researched immunization strategy to remove the vaccination barriers. To improve vaccine acceptance among people, false rumors and misconceptions about the COVID-19 vaccines must be dispelled (especially on the internet) and people must be exposed to the actual scientific facts.