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It is one of the important issues to investigate the vibration behavior of railway bogies, since the vibration of the bogies may result in loosening bolts which fix the parts to the bogie frames or/and fatigue fracture of the parts themselves. A technique for predicting the vibration of bogie parts is proposed by which the acceleration power spectral densities (PSDs) at evaluated points are predicted with the use of frequency response functions (FRFs) between the axle boxes and the evaluated points, together with the use of measured accelerations of axle boxes. Stationary excitation tests are conducted to identify the FRFs, and the axle boxes or rails were hit with impulse hammers to excite the bogies. Alternatively, the new approach without the stationary tests is also proposed in this study. In this case, the FRFs are identified with the accelerations acquired in the preliminary running tests in car depots. The proposed technique is applied to the vibration prediction of the bogies for several types of railway vehicles including electric cars and a diesel car, and the differences or ratio between the predicted and actually measured PSDs are evaluated. It is confirmed that the preliminary running tests are preferable to stationary excitation tests for improving the prediction accuracy. It is also verified that the prediction error can be reduced in the case where not only the vertical but the lateral and longitudinal accelerations of axle boxes are considered as the excitation inputs under the conditions that the principal component regression is applied to identify the FRFs.