Abstract: Solving an expanded order-system dynamic-equation is the difficulty to obtain the dynamic response of a random structure. By using Gegenbauer polynomial approximation, the calculation problem of dynamic responses of a random parameter system is transformed to system's response calculation of an equivalent order certainty expansion. The Precise Integration Method is used to obtain the K_L decomposition vectors of the non-stationary filtered white noise random excitation, with characteristics of energy concentration, a small amount of K_L vector used to compute response of the extended order system can obtain a very accurate result, and it significantly improves the calculation efficiency. Simulation verifies the correctness of the method, and the effects of the probability density function of random parameters to the response mean square value are studied, and some engineering valuable conclusions are obtained.