Suppression of the vertical bending vibration of carbodies has recently become essential in improving the ride comfort of railway vehicles. In this paper, we propose a method of controlling vibration in the primary suspension of rolling stock to reduce carbody vibration. Systems conceivable for this purpose include a semi-active suspension system with variable axle dampers that can control damping force continuously by command current to the damping force control valve. Based on LQG control theory, we carried out numerical simulations and performed excitation testing with a carbody equivalent to an actual Shinkansen vehicle fitted with variable axle dampers to selectively suppress the first mode bending vibration of the carbody. The results show that this LQG control method reduces the power spectral density (PSD) of acceleration on the floor more effectively than the sky-hook control method, which does not consider the vibration modes of the carbody.