For the multipleattribute decision making where the attribute values are represented by comparative linguistic expressions, an extended TOPSIS method based on possibility distribution was proposed. Firstly, the method transformed comparative linguistic expressions into hesitant fuzzy linguistic information and defined a new distance generated by possibility distribution to avoid error caused by traditional hesitant fuzzy linguistic distance formula. Next, a new TOPSIS method with possibility distribution distance is designed, which introduced the ranking index according to the concept that the chosen alternative should be as close as possible to the ideal solution and was better than traditional one to reflect the similarity scale. Finally, a numerical example using the proposed approach illustrates an application to evaluate the delivery service providers, in which the effectiveness and feasibility are verified.