  A notion of $n$-cotorsion pairs in an extriangulated category with enough
projectives and enough injectives is defined in this article. We show that
there exists a one-to-one correspondence between $n$-cotorsion pairs and
$(n+1)$-cluster tilting subcategories. As an application, this result
generalizes the work by Huerta, Mendoza and P\'{e}rez in an abelian case.
Finally, we give some examples illustrating our main result.
