Abstract: An equivalent excitation method for random structural vibration analysis is proposed. Based on the power spectral density of input excitation, an equivalent excitation is constructed, which is adopted as a determinate input load to calculate the responses of the structure, then these responses are decomposed to special responses corresponding to their specific pseudo-excitations, and the power spectral density of the responses is derived using the specific responses. The random vibration of a linear structure under one point non-stationary excitation is studied, and a case for a nonlinear structure is discussed.