  In this paper, first we classify non-abelian extensions of Leibniz algebras
by the second non-abelian cohomology. Then, we construct Leibniz 2-algebras
using derivations of Leibniz algebras, and show that under a condition on the
center, a non-abelian extension of Leibniz algebras can be described by a
Leibniz 2-algebra morphism. At last, we give a description of non-abelian
extensions in terms of Maurer-Cartan elements in a differential graded Lie
algebra.
