In hausdorff Local convex topological spaces, this paper deals with the equivalence problem of two kinds of proper efficiency for set-valued vector optimization. The strong efficiency and strict efficiency play the important roles in optimization theory. At present it is known that the strict efficiency is equivalent to the strong efficiency under the condition of convexity. The nearly cone-subconvexlikeness of set-value maps is a very important generalized convexity in optimization theory, this note obtained the equivalence of strict efficiency and strong efficiency under the assumption of nearly cone-subconvexlikeness, and this conclusion is the generalization of the result that the strict efficient points equal to the strong efficient points for convex set. The results obtained in this paper will enrich the optimization theory.