The COVID-19 outbreak has illustrated the wide range of issues that supply networks confront when they are subjected to major interruptions. The supply networks for vaccines are no exception. To get out of this pandemic, it's critical to identify and address problems with the COVID-19 vaccine supply chain (VSC). This work identifies 13 challenges and prioritizes those. The findings provide stakeholders and government policymakers with realistic advice for developing a better VSC. This paper proposes a methodology based on fuzzy analytical hierarchy process (Fuzzy-AHP) with the use of triangular fuzzy numbers for prioritizing VSC barriers. It has been found that the impact of poor health worker training facilities becomes maximum with the highest weightage. Moreover, the managerial implication of the results is also provided, which will be useful for VSC sectors to take suitable decisions to overcome these obstacles.