The worldwide COVID-19 pandemic sparked such a wave of concern that made access to vaccines more necessary than before. As the vaccine inaccessibility in developing countries has made pandemic eradication more difficult, this study has presented a mathematical model of a sustainable SC for the COVID-19 vaccine that covers the economic, environmental and social aspects and provides vaccine both domestically and internationally. It has also proposed a robust data-driven model based on a polyhedral uncertainty set to address the unjust worldwide vaccine distribution as an uncertain parameter. It is acceptably robust and is also less conservative than its classical counterparts. For validation, the model has been implemented in a real case in Iran, and the results have shown that it is 21% less conservative than its classical rivals (Box and Polyhedral convex uncertainty sets) in facing the uncertain parameter. As a result, the model proposes the construction of two domestic vaccine production centers, including Pasteur Institute and Razi Institute, and five foreign distributors in Tehran, Isfahan, Ahvaz, Kermanshah, and Bandar Abbas strategically. © 2022 Elsevier Ltd. All rights reserved.