Hesitant fuzzy linguistic sets is an extension of both linguistic term sets and hesitant fuzzy sets. Motivated by the idea of traditional Electre methods, an Electre method for hesitant fuzzy linguistic information is introduced. Firstly, the Hausdorff distance of hesitant fuzzy linguistic numbers are proposed. Then, the outranking relation for hesitant fuzzy linguistic numbers under each criterion is developed, based on which, a method for hesitant fuzzy linguistic multi-criteria decision-making based on the outranking relation is proposed. Finally, a numerical example is given to illustrate the effectiveness and feasibility of the proposed method.