Abstract: One of the key techniques for structural robust optimization is the probability characteristics analysis for structure responses such as calculations of their mean and variance values. Typically used methods include the Taylor series method, Monte Carlo simulation and numerical integration methods etc. The Taylor series method is not accurate when the variances of random parameters are large. On the other hand, Monte Carlo simulation and numerical integration methods are relatively accurate but computationally inefficient. To abate computational efforts, in this paper, the binomial series approximation for structural displacements is introduced into the Gauss-Hermite quadrate formula. By doing so, full finite element analyses are not needed at the integration points, thus the computational amount is reduced efficiently. The sensitivities of means and variances of displacements with respect to the mean values of input variables are also derived by the adjoint method. A numerical example is provided to demonstrate the effectiveness of the proposed method. The results are encouraging in terms of accuracy and efficiency.