In the design of Francis turbine runner, improvement of variable flow characteristics is one of the problems. Conventionally, performances at not only the design point but also non-design points were optimized using various optimization methods such as multi-objective genetic algorithm. However, since general Pareto ranking technique treats all objective function with the same priority, the solutions with high efficiency at non-design point but low efficiency at design point might be obtained. The highest efficiency point of such solutions would deviate from the design point, therefore, a technique to match those points is needed. In this study, we developed the Bayesian optimization system for Francis turbine runner design using computational fluid dynamics (CFD), Gaussian process regression (Kriging) model, and multi-objective genetic algorithm. To match the highest efficiency point and design point, non-swirling discharge of each solution was evaluated from CFD results, and a constraint was considered using the discharge predicted by Kriging model. Finally, it was confirmed that the solutions obtained by Bayesian optimization with the constraint of non-swirling discharge is superior to the one without the constraint.