In this paper, a class of B-preinvex functions introduced by Bector et al. \cite{BSL} are considered. Necessary and sufficient conditions, under which a locally Lipschitz function is B-preinvex, are established in terms of the Clarke subdifferentiable. Moreover, a sufficient optimality condition of efficient solution for a nonsmooth multiobjective programming problem involving B-preinvex functions is obtained. Finally, weak and strong duality theorems are proved for Mond-Weir type dual under B-preinvexity assumption.