In this paper, Kriging model is applied to a constrained multi-objective optimization problem. In order to balance the local and global search in the Kriging model, the criterion 'expected improvement (EI)' is adopted. Probability of satisfying the constraints is calculated in the Kriging model to impose the constraint effect into EL Search region of the design space is modified during the optimization by investigating the distribution of the design variables. Functional analysis of variance (ANOVA) is performed to identify which design variables are important for the objective and constraint functions. The present method is applied to a transonic airfoil design for the validation.