This work is the first attempt to decompose the positron annihilation lifetime spectrum into the form of a frequency spectrum by Fast Fourier Transform (FFT) technique. Each real peak in the frequency spectrum indicates a lifetime component. The peak position corresponds to the annihilation constants, the peak area is proportional to the intensity of the component. The principle of this method is described in this paper. We thoughtfully consider the effects of the instrumental resolution function and the statistical error. A program is compiled with Turbo C and successfully operated on PC ALR-286. The analysis results for some simulated spectrum are satisfactory. The work indicates that the advantages of this method are its simplicity, rapidity, less effect of the instrument resolution function and no guessing what the components are before analysis.