The changes of reflection spectrum and dispersion of fiber Bragg grating(FBG) apodized by moiréeffect are analyzed theoretically. It is pointed that the apodization of the fiber grating by using Moiréeffect is a pure apodization because the Moiré effect makes the index modulation amplitude in both positive and negative sides and keeps the average index unchanged. However, there exist some side lobes in short wavelength side of Bragg peak when the fiber Bragg grating was apodized by conventional raise cosine function because of the F-P effect. Experimentally apodized FBG by using Moiréeffect was obtained with a side mode suppression 6 dB better than conventional FBGwithout apodization.