Granularity structure analysis and granularity information measurement are important tools to study the complicated information system. Based on the dual hesitant fuzzy relation, this paper proposes the dual hesitant fuzzy granular structure, and discusses three kinds of partial-order relations on the granular structure. At the same time, the nesting relationship between partial order relations is studied. On the basis of dual hesitant fuzzy granular structure, dual hesitant fuzzy information entropy is defined and its related properties are verified.