A surrogate model is generally built based on the high fidelity simulations.However, the amount of the high fidelity data simulated is usually not enough to represent the design space because the evaluation of the high fidelity data is very expensive.To avoid this problem, researchers have studied on multi-fidelity modeling that uses two models of different fidelities to efficiently generate a surrogate model.In the multi-fidelity modeling, a high fidelity model is accurate but requires a large computational cost for evaluation.On the other hand, a low fidelity model requires small computational cost but has low accuracy compared to the high fidelity model.Thus, it is important in multi-fidelity modeling how to build a multi-fidelity model that best combines a low fidelity model and high fidelity data in constructing a surrogate model.Among many proposed multi-fidelity models, the most accurate model is known to be a high fidelity model constructed by a low fidelity Gaussian process model, y1, (x), multiplied by a scale factor ρ plus a Gaussian process, δ(x), which represents the difference between ρy1 (x)and high fidelity data.There exist four such models [1-4].