Actively responding to climate change and accelerating the realization of carbon emission reduction are the common goals of global sustainable development. Hydrogen energy, as a “zero carbon emission” secondary energy, is playing an increasingly important role on the world energy stage. Hydrogen energy infrastructure (focusing on hydrogen refueling stations) is a key infrastructure in the transition to a hydrogen economy. However, the indicators that influence the location selection of hydrogen refueling stations (HRSs) are specific and have complex relationships, and current research still lacks a comprehensive analysis of its location selection decision-making indicators. Based on this research gap, this study proposes a hybrid fuzzy decision-making approach to determine the relationship and degree of influence between indicators. Firstly, this study identified 18 decision indicators that influence location selection from four dimensions: policy, economy, society, and environment. Subsequently, semi-structured interviews were used to initially assess the relationship between indicators. Finally, by using interpretive structural modeling and the fuzzy decision-making trial and evaluation laboratory (ISM-FDEMATEL), a 7-level structural model is established, which clarifies the complex relationship between indicators and the individual attributes of each indicator. The research results show that the indicators of the policy dimension have a more significant influencing degree than the other three dimensions and have a greater influence on the entire indicator system; the indicators of the economic dimension have a higher influencing degree and are easily influenced by other indicators. These findings will benefit policymakers and practitioners to prioritize and manage their resources effectively and efficiently and provide a valuable reference for advancing the sustainable development of the infrastructure for hydrogen energy.