Nowadays, sustainable material selection is an important issue for construction industry because of considering the environmental and social competencies according to quality and cost targets. Hence, multi criteria group decision making (MCGDM) is a known powerful tool to select the best potential alternatives based on group assessment of decision makers (DMs) in complex realworld cases. In traditional MCGDM methods, the relative significance of each criterion and the performance evaluating of potential alternatives are considered precisely. However, when the complexity of the real-world systems related to humans is increased, the future information of them cannot be precise / known completely. In this respect, decision making problems are one of the science fields that the information is often vague / uncertain. Moreover, If DMs cannot assign their opinions by expressing the linguistic terms regarding to the classical fuzzy sets, the Interval-Valued Hesitant Fuzzy Sets (IVHFSs) theory is a useful tool to help the DMs in these hesitant conditions and can present a more practical and accurate modeling. In this study, an Interval-Valued Hesitant Fuzzy Preference Selection Index (IVHF-PSI) method is presented to solve the sustainable cement block selection problems in construction industry. Finally, the process of the proposed IVHF-PSI method is performed by considering a real case study to represent the applicability and verification of the proposed approach.