In this paper, the authors present the multi-criterion stochastic optimal selection of a double glazing system for a given office building. Four elements are required for a multi-criterion stochastic optimal design: an accurate and fast simulation model, an optimization solver, correct handling of the multi- criterion decision problem, and consideration of the stochastic performance quantification. Since stochastic optimal design is a double-exponential problem, the Gaussian Process (GP) emulator, as a surrogate to EnergyPlus, was used to achieve computational efficiency. The GP emulator was derived based on the training set generated from EnergyPlus simulation runs. A genetic algorithm and Pareto optimality were then applied to deal with the multi-criterion optimization. Stochastic performance quantification was performed using a stochastic objective function and Latin Hypercube Samplings (LHS). Using the aforementioned four elements, the authors realized the multi-criterion stochastic optimal design of a double glazing system. The differences in the mean values of energy consumption and PMV between EnergyPlus and both GP emulators are 0.27 (kWh/m2) and 0.16 (kWh/m2), respectively, and 0.01 and 0.00, respectively. In addition, 13 non-dominated Pareto optimal solutions were successfuly obtained. The approach presented in this paper improves computation efficiency for a multi-criterion stochastic optimal design problem and contributes to higher-fidelity simulation-based decision making.