•Propose some formulae to calculate the gain and loss for unbalanced HFLTSs.•Extend the TODIM method to deal with MCGDM problems with unbalanced HFLTSs.•Provide three applications to demonstrate the proposed TODIM method. Uncertainty and impreciseness usually exist widely in decision making problems nowadays. When eliciting assessments over alternatives, decision makers tend to have some hesitancy and thus provide hesitant fuzzy linguistic term sets (HFLTSs). Moreover, the unbalanced linguistic term set sometimes has advantages over the balanced one for dealing with practical linguistic decision making problems. The purpose of this paper is to develop a new method to deal with multi-criteria group decision making (MCGDM) problems with unbalanced HFLTSs by considering the psychological behavior of decision makers. To achieve this goal, some formulae are first proposed to calculate the gain and loss for an unbalanced HFLTS over another. As a special case of the unbalanced HFLTS, the formulae of gain and loss for a balanced HFLTS are also provided. Afterwards, the classical TODIM method is extended to develop a new MCGDM method based on unbalanced HFLTSs. Eventually, the proposed method is demonstrated by using three practical applications, including a personnel selection process, an investment alternative selection process and a telecommunication service provider selection process.