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Dual hesitant fuzzy sets, encompassing fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy sets, and fuzzy multisets as special cases, are very useful in dealing with uncertainty considering the membership and nonmembership degrees by a set of possible values. This paper aims to develop a prioritized multi-attribute decision-making method to solve dual hesitant fuzzy decision problems. We first propose a correctional score function of dual hesitant fuzzy elements (DHFEs) for characterizing hesitant degrees in DHFEs more effectively. Then we apply the correctional score function and the dice similarity measure of dual hesitant fuzzy sets (DHFSs) to solve multi-attribute decision-making problems in which the attributes are in different priority levels and the attribute values take the form of DHFEs. Finally, an illustrative example is employed to show the feasibility of the proposed method in its practical applications.