This paper presents an application of the model reduction for the wheelset of the railway vehicle from the best optimal Hankel-norm approximation. It is necessary to reduce the complexity of the control synthesis by model reduction techniques since the wheelset model is highly interactive with high order. The proposed approach solves the best optimal solution layer by layer from any optimal solution of each layer. This approach adopts the left inverses of inner function vectors characterized from the Schmidt pair. The McMillan degree of the reduced-order model for the successive layer can be determined. Fuerthermore, this successive layer will also become another approximation problem. This paper also proposes an algorithm to calculate the best optimal approximation recursively. The best optimal Hankel-norm approximation will be compared with the other optimal Hankel-norm approximation in frequency domain for the transfer function matrix and all its arrays. The results reveal that the best optimal Hankel-norm approximation is better in sense of the singular values not only in all layers but in all arrays.