Abstract: According to linear characteristics of the relation between the input and output of linear dynamic systems, the time domain method is investigated for random vibration analysis of structures subjected to non-stationary random excitations. Equations of motion of the structure are first transformed into the form of state equations, and non-stationary random excitations are discretized into random vectors at a series of time points. The state equations derived are then solved by means of a high precision direct integration method, which yields an explicit linear expression of the structure responses by the random vectors at different time points. Based on the above explicit expression, mean values and variances of the structure responses at different time points are obtained through the calculation rules of the first order moments and the second order moments. On the other hand, Monte-Carlo numerical simulation can be conducted by use of the explicit derived expression, which not only provides mean values and variances of the random responses, but also gives the evolutionary probability density function of the non-stationary responses. Numerical examples show that the proposed methods have high accuracy and efficiency and have no restrictions on the forms of the random excitations.