Abstract: By introducing a class of convex constrained optimization problems with uncertain data, we first established a MondWeir type robust approximate dual problem for the uncertain convex constrained optimization problem by means of  robust optimization method. Then, by means of a class of generalized robusttype approximate KKT conditions, we characterized approximate duality relationship between the uncertain convex constrained optimization problem and its Mond\|Weir type robust approximate dual problem.

Key words: uncertain optimization problem, approximate duality, robust KKT condition