Hesitant fuzzy linguistic term set (HFLTS) is a very useful technology in dealing with decision‐making problems where people have hesitancy in providing their linguistic assessments. Distinct methods have been developed to aid decision making with HFLTSs, yet there is little research involving the issue that how to deal with the multigranularity hesitant fuzzy linguistic information. The aim of this paper is to develop the aggregation method for multigranularity hesitant fuzzy linguistic information and solve the linguistic group decision problem with different linguistic term sets. To do so, we first modify the translation functions and aggregation operators in the existing 2‐tuple linguistic representation models so as to aggregate linguistic terms from different linguistic term sets. Then, we introduce the notion of hesitant 2‐tuple sets to make computation of HFLTSs without loss of information, and develop some new operators to aggregate HFLTSs from different linguistic term sets. Using these operators, we propose a method to deal with multigranularity linguistic group decision‐making problems with different situations where importance weights of either criteria or experts are known or unknown. Finally, the multigranularity linguistic group decision‐making model is implemented to the healthcare waste treatment in West China Hospital to validate its effectiveness and efficiency in aiding decision‐making process.