Recently, the duct system with a cross flow fan was used to improve the ventilation in various industrial fields. For the efficient ventilation, it is necessary to design the duct system based on the flow characteristics around the cross flow fan. In the present study, the flow characteristics around a cross flow fan in the ventilation duct were predicted by using the moving mesh and sliding interface techniques for the rotation of blades. To design the duct system with the high performance of ventilation, the CFD simulations were repeated with the revised duct model based on the DOE. With the numerical results of flow rate through the ventilation duct with various geometric parameters, the optimized geometry of ventilation duct to maximize the flow rate was obtained by using the Kriging approximation method. From the performance curves of cross flow fan in the original and optimized models of ventilation duct, it was observed that the flow rate through the optimized model is about 16 percent larger than that through the original model.