Recently world is passing through a deadly pandemic called COVID-19. A global pandemic that was introduced or some say produced first in Wuhan, CHINA, and within some months spread around the world creating chaos in people's minds because mankind had not seen such kind of virus in decades. Spending life in hard lockdown and keeping social distance affects people's mental health and behavior. Within a year by the blessing of science, vaccines were introduced by different profitable and non-profitable organizations of different countries around the globe to fight back against the deadly virus. Due to mental health and behavior issue some peoples refuse to take the vaccine and also discoursed other people. Most of the activity happened on social media platforms like Facebook, and Twitter because of less monitoring. This effected the decision of people to take the vaccine as the vaccine is not taken as expected. On the other hand, some people express the benefit of talking about vaccines. In this paper, The Facebook comment that was posted related to covid-19 vaccine and vaccination campaign and tried to analyze the sentiment on covid-19 vaccine of people of Bangladesh has been examined. Due to the fact that Facebook comments allow users to voice their opinions, a dataset has been prepared from these comments. Dataset contained 1700 entries of Bangla comments and was labeled each entry with the corresponding sentiment from positive, negative, or neutral. Bangla comment was converted into numerical value by using the tokenizer method and performed various machine learning and deep learning algorithm on 1300 dataset which were where the LSTM algorithm appears as the best fit with an accuracy of 92.27%. LSTM works perfectly in the dataset containing Bangla comments.