In order to solve the frequency reliability robust design problems of the random dynamic structural system with arbitrary distribution parameters, the formulas of frequency reliability and its sensitivity are obtained by the Edgeworth series method, which can make the unknown probability distribution functions expanded into the standard normal distribution. Probability distribution type is not any restricted in the condition that the first four moments of the random parameters are known, which is more closed to the engineering practice. Furthermore, the frequency reliability-based robust method of the random dynamic structural system is obtained by the robust and the optimization technology on the basis of frequency reliability and sensitivity design, which helps designers to establish acceptable parameter values and to determine the fluctuations of the parameters for the safe operations. Moreover, combining theoretical method and engineering practice, a numerical example of the random axial vibration of rod system with arbitrary distribution is provided, which demonstrates the efficiency and accuracy of the proposed method.