This paper proposes a method to determine weight vector of attributes with linear prioritization relationship and the assessment values are represented by hesitant fuzzy elements. The weight associated with an attribute depends upon the satisfaction of an alternative for the higher priority attribute. First, some hesitant fuzzy prioritized aggregation operators are defined and their desirable properties are discussed. These proposed operators can capture the prioritization phenomenon among the aggregated hesitant fuzzy elements. Then, we develop a multi-attribute decision-making (MADM) method based on the proposed operators in hesitant fuzzy environment. Finally, a practical example is provided to demonstrate the effectiveness of the developed method and make a comparative analysis on generalized hesitant fuzzy prioritized aggregation operators in decision-making.