The availability of vaccines provides a promising solution to containing the COVID-19 pandemic . Here, we develop an epidemiological model to quantitatively analyze and predict the epidemic dynamics of COVID-19 under vaccination . The model is applied to the daily released numbers of confirmed cases of Israel and United States of America to explore and predict the trend under vaccination based on their current epidemic status and intervention measures . For Israel, of which 53.83% of the population was fully vaccinated, under the current intensity of NPIs and vaccination scheme, the pandemic is predicted to end between May 14 , 2021 to May 16 , 2021 depending on an immunity duration between 180 days and 365 days; Assuming no NPIs after March 24 , 2021, the pandemic will ends later, between July 4 , 2021 to August 26 , 2021 . For USA, if we assume the current vaccination rate (0.268% per day) and intensity of NPIs, the pandemic will end between February 3 , 2022 and August 17 , 2029 depending on an immunity duration between 180 days and 365 days . However, assuming an immunity duration of 180 days and with no NPIs, the pandemic will not end, and instead reach an equilibrium state with a proportion of the population remaining actively infected . Overall the daily vaccination rate should be chosen according to the vaccine efficacy and the immunity duration to achieve herd immunity . In some situations, vaccination alone cannot stop the pandemic, and NPIs are necessary both to supplement vaccination and accelerate the end of the pandemic . Considering that vaccine efficacy and duration of immunity may be reduced for new mutant strains, it is necessary to remain cautiously optimistic about the prospect of the pandemic under vaccination.