One of the constant concerns in public and private organizations is choosing a project from among the multitude of potential projects to be implemented. Due to the limited resources in different sectors, projects should be prioritized in order to obtain the maximum benefit. In national and government projects, it is not necessarily important to pay attention to financial components, and more dimensions should be considered. Sustainability is a component that considers various economic, environmental, and social aspects in the evaluation of projects. In this regard, in this study, the main goal is to evaluate and select rail transportation projects according to sustainability criteria. In general, 15 indicators were identified in three economic, environmental, and social sectors, which were weighted using the best–worst fuzzy method (FBWM). The most important indicators in the evaluation of projects are the investment cost, the rate of internal return from a national perspective, and the lesser impact of the plan on environmental destruction. According to the weighted indicators, the stochastic VIKOR approach is developed for the first time in this article, which was evaluated according to two scenarios of demand changes and cost changes of candidate projects. In the stochastic VIKOR approach, to deal with uncertainty, different scenarios are defined, through which it is possible to respond to different conditions and evaluate projects more realistically. Validation of this method is compared to other multi-criteria decision-making methods. The main contribution of this study is presenting the stochastic VIKOR approach for the first time and considering the uncertainty in project evaluation. The findings show that the projects that have the most economic gains from the national and environmental aspects are selected as the best projects.