The use of hydrogen storage technology (HST) as a bridge for producing and utilizing hydrogen energy in the hydrogen industry chain is significant, and its evaluation has attracted the interest of researchers. Since there are different types of HSTs, selecting the most appropriate one requires the participation of plenty of experts with different professional backgrounds, which makes this be modeled as a large group decision-making problem. This paper develops a reliability-driven large group consensus decision-making (LGCDM) method for HST selection using the hesitant fuzzy linguistic terms set (HFLTS) as the evaluation representation format. Specifically, the expertise level of individuals and the reliability of group opinions are measured based on the set variables, and then the dimensionality of large groups is reduced based on the reliability of subgroup opinions. Furthermore, an opinion reliability rating mechanism is designed and, when consensus is not satisfactory, a feedback recommendation mechanism and consensus optimization mechanism are developed for implementation. Finally, the proposed reliability-driven LGCDM approach is applied to the HST selection for THVOW Company, and the comparison with existent related approaches indicates that it not only is practical and reasonable, but also provides a technical path for relevant departments to make decisions on practical issues.