［Purposes］To study the characterization of the emptiness of efficient solution set and properly efficient solution set for multiobjective optimization problems based on Benson’s method. ［Methods］By using the scalarization method and the density results to study the characterization of the emptiness of the efficient solution set and the properly efficient solution set of multiobjective optimization problems. ［Findings］Firstly, obtaining the equivalent characterization of unbounded Benson scalarization problem under natural cone order, and on this basis, giving the necessary conditions that the efficient solution set and the properly efficient solution set of multiobjective optimization problem are empty sets. Secondly, obtaining the conditions that the efficient solution set and the Borwein properly efficient solution set under dictionary order are empty sets, and give examples to illustrate the assumptions. Finally, the necessary conditions for the unbounded Benson scalar problem under the general cone order are given, and the relationship between the effective solution of the multiobjective optimization problem and the optimal solution of the Benson scalar problem is also given. ［Conclusions］For convex and nonconvex multiobjective optimization problems, the emptiness of solution sets is characterized.