Abstract: In this paper, some different properties of the subdifferential for set-valued mappings, which has been introduced in ``Subgradient of S-convex set-valued mappings and weak efficient solutions"(Appl. Math. J. Chinese Univ., 1998, 13(4): 463-472)  are discussed. Moreover, in virtue of the property of the contingent derivative, some exact calculus rules of the subdifferential for calculating the subdifferential for the sum, composition and intersection of two set-valued mappings. Finally, a necessary and sufficient optimality condition of set-valued optimization problems is discussed.