The efficient global optimization method is a global optimization technique based on the stochastic kriging model to efficiently search the global optimum in a design space. Efficient global optimization selects the next sample point in the view of the probability that a global minimum is located. To present the probability, the efficient global optimization method introduces the expected improvement function. The mean and variance at the untried point provided from the kriging model are used to calculate the expected improvement function. Efficient global optimization selects the maximum expected improvement point as the next sample point. After validating the efficient global optimization method by several test functions, we applied it to a diffusing S-duct shape design problem which needs a computationally expensive turbulent computational fluid dynamics analysis. The design objective is to improve the total pressure recovery of the S-duct. The improved S-duct shape was searched globally through the efficient global optimization method. Our results confirmed that the efficient global optimization method can efficiently provide a meaningful engineering result in the S-duct shape design.