Abstract: Compared with the time-domain method, the frequency-domain method is a more efficient and easy-to- implement method for random vibration analysis. However, the existing frequency-domain methods often involve truncation for degree of mode or decomposition of the power spectrum in multi-correlation conditions, which may have impact on the computational accuracy and efficiency of the methods. To this end, an accurate and efficient auxiliary harmonic excitation generalized method is proposed for the analysis of random vibration of linear structures under stationary Gaussian excitation in the framework of the frequency domain method. First, the concepts of generalized impulse response function and generalized frequency response function are introduced, and a generalized analysis method, which is equivalent to the complete quadratic combination method of response power spectrum calculation, is derived. Secondly, replacing the product of generalized frequency response function by the product of response of auxiliary harmonic excitation, a more easily implemented auxiliary harmonic excitation generalized method is further proposed based on generalized analysis method. Third, according to the different calculation methods of response for structure under the auxiliary harmonic excitation, two generalized methods of auxiliary harmonic excitation generalized method with different applicability are proposed, namely, the auxiliary harmonic excitation generalized method based on the mode superposition and the auxiliary harmonic excitation generalized method based on the time analysis. Meanwhile, the computational performance of the above two methods and their comparative analysis with the existing methods are introduced. Finally, the computational accuracy and efficiency of the proposed method are verified by two examples. The results of the examples show that the auxiliary harmonic excitation generalized method has significant advantages of the calculation efficiency over the complete quadratic combination method and the pseudo-excitation method with the same calculation accuracy.