Abstract: Based on previous studies, a simulation method for multi-point ground motion time histories is developed. Employing the square root operation of complex power spectral density matrix, the paper defined the complex power spectral density matrix as the product of Hermite matrix and its conjugate transposed matrix. Meanwhile, the relationship between amplitudes, phase angels of simulated ground motions and the element of the Hermite matrix was given. In addition, the variation of the amplitude of white-noise bedrock acceleration was taken in account, which makes this method more suitable for the simulation of the multi-point ground motions of long-span structures.