In this paper, a multi-objective design optimization for a three-element airfoil consisted of a slat, a main wing, and a flap was carried out. The objective functions were defined as the maximization of lift coefficient at landing (C18) and near stall (C120)conditions simultaneously. Genetic Algorithm (GA) was used as an optimizer. Although it has advantage of global exploration, its computational cost is expensive. To reduce the computational cost, the kriging model which was constructed based on several sample designs was introduced. The solution space was explored based on the maximization of Expected Improvement (EI) value corresponding to objective functions on the kriging model to consider the predicted value by kriging model and its uncertainty. The improvement of the model and the exploration of the optimum can be advanced at the same time by maximizing El value. In this study, 90 sample points are evaluated using the Reynolds averaged Navier-Stokes simulation (RANS) for the construction of the kriging model. Through the present exploration process, several designs were obtained with better performance than the baseline setting in each objective function. Functional Analysis of Variance (ANOVA) which is one of the data mining techniques showing the effect of each design variable on the objectives is applied. Main-effects of the design variables are calculated to recognize which design variable has the effect on the objective functions. This result suggests that the gap and the deflection of the flap have a remarkable effect on each objective function and the gap of the slat has an effect on C120.