By utilizing the Levinson-Durbin algorithm of modern spectral estimation, the parameters of AR filter with demanded correlation spectrum can be obtained. The output of the filter with the input of white Gaussian random sequences, and its shift sequence then form a pair of Gaussian random sequences with the demanded correlation coefficients, which can meet the occasions of correlated Rayleigh fading channels in wireless communication and radar systems. Finally the validity of the method is proved by simulation results.