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Fuzzy multi-criteria decision-making (MCDM) methods are useful and reliable for multi-criteria selection problems under uncertain and imprecise situations. In these methods, if decision-makers hesitate among several linguistic terms, hesitant fuzzy linguistic term sets (HFLTSs), represented by a set of successive linguistic terms instead of single linguistic terms, may be more appropriate to make evaluations. The notion of a fuzzy envelope for the HFLTSs is a beneficial tool that can be directly applied to fuzzy MCDM methods to elicit comparative linguistic expressions (CLEs). The aim of this study is to present a methodology that combines the fuzzy CODAS (COmbinative Distance-based Assessment) method with the fuzzy envelope of HFLTs based on CLEs to solve a personnel selection problem. In order to examine the feasibility of the presented methodology, a case study on blue-collar personnel selection in a manufacturing firm is conducted. A sensitivity analysis is performed to demonstrate the stability and validity of the ranking results. Furthermore, the ranking results of the presented methodology are compared with various fuzzy MCDM methods, including fuzzy EDAS, fuzzy TOPSIS, fuzzy WASPAS, fuzzy ARAS, and fuzzy COPRAS. The results show that the presented methodology is efficient and stable for solving personnel selection problems in a hesitant fuzzy environment.