The X-ray diffraction patterns of a Fibonacci series consisted of two kinds of atoms have been simulated according to the amplitudes summed up with phases. Peaks appeared at K=(m+nt)/(1+2t)d-1, where d is the average planar distance. Relationship between the anglewidth β of diffraction peaks and the total thickness of atomic layers obeys the Scherrer for-mula: β=(0.88λ)/(Dcosθ), just as that for crystals. The intensities of weak diffraction peaks ch-anged irregularly with the increasing number of atomic layers, which can be illustrated by zigzag path in the amplitude-phase diagram.