In process design, the values of design variables X for equipment and operating conditions should be optimized for entire processes, including all unit operations, such as reactors and distillation columns, to consider effects between unit operations. However, as the number of X increases, many more simulations are required to search for the optimal X values. Furthermore, multiple objective variables Y, such as yields, make the optimization problem difficult. We propose a process design method based on adaptive design of experiments and Bayesian optimization. Optimization of X values that satisfy target values of multiple Y variables are searched, and simulations for the optimized X values are then repeated. Therefore, X will be optimized by a small number of simulations. We verify the effectiveness of this method by simulating an ethylene oxide production plant.