Massive vaccination is very important to end the coronavirus disease 2019 (COVID-19) pandemic. This study determined the willingness to receive a COVID-19 vaccine by the university students of Bangladesh and identified their apprehension about the effectiveness and safety of COVID-19 vaccines. Students were invited to complete an online cross-sectional survey (April 3 to June 10, 2021) to explore the intention to receive a COVID-19 vaccine and other factors regarding the responsiveness of the COVID-19 vaccine. Among the 191 respondent students, 52.9% willingly agreed to receive a vaccine, where the remaining was either not decided yet (27.7%) or was not intended to get vaccinated (15.7%). The odd of getting a vaccine were only 1.15. About 83.2% of students were conscious about the severity of COVID-19 and many students responded that they are well-versed about vaccine activity (67.5%) and risk factors (66%). Among the approved vaccines, most students preferred the Oxford-AstraZeneca COVID-19 vaccine ChAdOx1 (38.7%) and Pfizer-BioNTech COVID-19 vaccine BNT162b2 (34%). As some of the students still have lesser intent to accept vaccines, public health officials need to be more proactive to focus on vaccine safety and benefits to enhance vaccine coverage among university students of Bangladesh.