This paper introduces a new non-stationary random vibration technique for the analysis of time-dependent random vibration systems. It is based on the pseudo-excitation method (PEM) and precise integration method (PIM), which is extended herein and can improve significantly the analysis efficiency. Based on the random vibration equations with the right-hand side random replaced by a pseudo excitation, the first and second orders of sensitivity formulae are calculated conveniently by differentiating these equations. By use of sensitivity information, the optimization of complicated random vibration can be performed easily. Some numerical examples of vehicle-bridge time-dependent coupled system show the effectiveness and accuracy of present method.