Abstract: By studying the categories of Leibniz algebras and Leibniz n -algebras, functors between them are established. Subsequently, the concept of an n -Nijenhuis operator and its dual notion on Leibniz algebras are introduced. Finally, the cohomology of n -Nijenhuis structures on Leibniz n -algebras is constructed via cochain complexes and cochain maps, and the corresponding cohomology groups are obtained.