  The aim of this paper is to provide cohomologies of $n$-ary Hom-Nambu-Lie
algebras governing central extensions and one parameter formal deformations. We
generalize to $n$-ary algebras the notions of derivations and representation
introduced by Sheng for Hom-Lie algebras. Also we show that a cohomology of
$n$-ary Hom-Nambu-Lie algebras could be derived from the cohomology of
Hom-Leibniz algebras.
