Limited by the writing mode, the real refractive index distribution of the long period fiber grating (LPG) is different from that of the classic theory, which makes the spectrum of the real grating disagrees with ideal value. Fourier series is used to analyze the harmonics of Gaussian refractive index. Effect on the harmonics distribution caused by the relation between the beam size and grating constant is summarized, and the principle of optimum parameter selection is discussed. And some conclusions about LPG fabrication and character estimation are gotten. The transmission spectrum comparison between the long cyde grating written point by point with Gaussian beams and transmission by amplitude mask is obtained.