Hesitant fuzzy entropy is an important tool for depicting the uncertainty degree of hesitant fuzzy set. In order to solve the shortcomings of the existing hesitant fuzzy entropies, the axiomatic definition of hesitant fuzzy entropy is proposed based on hesitant fuzzy set, and the parametric hesitant fuzzy entropy is constructed. Secondly, some numerical examples are given to compare the new parametric hesitant fuzzy entropy with the existing fuzzy entropies. The results show that the proposed entropy can describe the uncertainty degree of information more flexibly and effectively. Then, the application of parametric hesitation fuzzy entropy in multi-attribute decision-making problem is explored. The proposed entropy is used to determine the weight of the attribute. Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) and fractional function are adopted to present a method to solve the optimal scheme selection problem. Finally, an example is used to verify that the parametric hesitation fuzzy entropy and the proposed decision method has some practicability and feasibility.