Abstract: A method for generating a pseude random sequence having both specified amplitude probability distribution and desired spectral property is introduced in this paper. This method is suited to be used in a general digital computer. A pseudo-random sequence with perfect satisfactory power spectrum is obtained by FFT first and is used as a refrence sequence. Then a fundamental sequence with specified amplitude distribution is made to have the same spectral property as that of the refrence one by correlation transfer method （CT）. The relationship between the performance of FFT-CT method and the sample number of a sequence is studied in the paper. Some examples of simulating noise processes which have certain amplitude distributions and desired spectra properties are given.