  In this paper, we introduce the notion of a derivation of a Hom-Lie algebra
and construct the corresponding strict Hom-Lie 2-algebra, which is called the
derivation Hom-Lie 2-algebra. As applications, we study non-abelian extensions
of Hom-Lie algebras. We show that iso- morphism classes of diagonal non-abelian
extensions of a Hom-Lie algebra g by a Hom-Lie algebra h are in one-to-one
correspondence with homotopy classes of morphisms from g to the derivation
Hom-Lie 2-algebra DER(h).
