：According to the 1/4 vehicle body four-degree-of-freedom vertical vibration model of high-speed train,using the theory of random vibration and residue theorem,the root mean square value analytical formulae describing the dynamic response of railway vehicles to random excitations generated by vertical track irregularities are established. The correctness of the analytical formulae is validated by numerical calculation. The results show that the values computed are completely consistent with that simulated in a certain range of effective digital. Furthermore,the reliability of the analytical calculation method is validated by comparison with the whole vehicle simulation. The results show that the maximum relative deviation of the body vertical RMS acceleration computed and simulated is only 12.50%,the maximum relative deviation of the secondary suspension vertical RMS stroke computed and simulated is only 15.47%,thus,the analytical calculation method established is reliable. Based on this,using the golden-section adaptive,the damping design method of secondary vertical suspension is built. This research provides a reference for the initial design of the secondary vertical suspension system parameters of high-speed train.