Duality is of great importance in mathematical programming, since it allows to study a minimization problem through a maximization problem and to know what one can expect in the best case and has resulted in many applications. The aim of this paper is to establish the duality theorems for a kind of nonconvex constraint set-valued optimization problems. Based on the notion of invexity in terms of cone-approximating multifunction for a set-valued map, Mond-Weir and Wolfe dual problems are investigated for a primal constraint set-valued optimization. By employing the analytic method, the weak duality theorems, the strong theorems and the converse duality theorems between Mond-Weir and Wolfe dual problems and the primal constraint set-valued optimization problem are established in sense of weak efficiency. These duality theorems disclose that there exist the precise dual relationships between the primal optimization and the involved dual problems. The results obtained in present paper enrich and deepen the theory and applications of set-valued optimization.