Dynamic-reliability-based design optimization is a reasonable framework for the optimization of stochastic dynamical systems. In the present paper，a method is proposed for solving dynamic-reliability-based design optimization problems where design variables are considered as the mean values of the probability density functions of part of the random variables involved in the system. In this method，the reliability of stochastic dynamical system is evaluated efficiently by the probability density evolution method（PDEM）. Then，by performing the changes of probability measure（COM），the sensitivity of the dynamic reliability with respect to design variables can be efficiently estimated without any additional structural analysis. By incorporating the PDEM-COM synthesized method into a globally convergent version of the method of moving asymptote，dynamic-reliability-based design optimization problems can be solved efficiently. The effectiveness of the proposed method is verified by two numerical examples. The results of the numerical examples indicate that the proposed method is efficient and robust.