Global vaccination coverage is an urgent need to recover the recent pandemic COVID-19. However, people are concerned about the safety and efficacy of this vaccination program. Thus, it has become crucial to examine the knowledge, attitude, and hesitancy towards the vaccine. An online cross-sectional survey was conducted among university students of Bangladesh. Total of 449 university students participated. Most of these students used the internet (34.74%), social media (33.41%), and electronic media (25.61%) as a source of COVID-19 vaccine information. Overall, 58.13% and 64.81% of university students reported positive knowledge and attitude towards the COVID-19 vaccine. 54.34% of these students agreed that the COVID-19 vaccine is safe and effective. 43.88% believed that the vaccine could stop the pandemic. The Spearman's Rank correlation determined the positive correlation between knowledge and attitude. The negative correlation was determined between positive knowledge and hesitancy, and positive attitude and hesitancy. University students with positive knowledge and attitude showed lower hesitancy. Multiple logistic regression analyses determined the university type and degree major as the predictors of knowledge, whereas only degree major was the predictor of attitudes. 26.06% of the study population showed their hesitancy towards the vaccine. University type and degree major were also determined as predictors of this hesitancy. They rated fear of side effects (87.18%) and lack of information (70.94%) as the most reasons for the hesitancy. The findings from this study can aid the ongoing and future COVID-19 vaccination plan for university students. The national and international authorities can have substantial information for a successful inoculation campaign.