Based on the hesitant fuzzy linguistic theory, this paper proposes a hesitant fuzzy linguistic PROMETHEE method for multiple criteria decision making, in which all the judgments of alternatives over the criteria are represented by the hesitant fuzzy linguistic term set. An example concerning the Sichuan liquor brand evaluation is provided to demonstrate the applicability of the proposed method. The results of the numerical example show that the hesitant fuzzy linguistic term set has many advantages in describing and tackling the complex Sichuan liquor brand evaluation and decision-making problem with qualitative information. It also demonstrates that the introduced algorithm is easy to use, and the improved prepference functions ensure the scientific nature of the decision-making process and the accuracy of the decision results, as they allow decision-makers to select parameters according to their needs for representing strict preferences.