Abstract: In this paper,we firstly introduce the concept of ε-strongly effective point set with constraint in locally convex Hausdorff topological vector space. Then, under the conditions that the feasible region is arcwise connected and compact, and the objective function is k-arcwise connected set-valued mapping, we prove the ε-stronglyeffective point set is nonempty, and obtain the connectedness of ε-strongly efficient solution set with constraints.