A new method for fabricating apodised fiber Bragg gratings (FBG) without self induced chirp is proposed by adjusting the period with the depth of refractive index modulation, in which general coupling coefficient is kept nearly constant along the grating. And effective medium picture is used to analyse the mechanism why self-induced chirp is eliminated by this method. Compared with that with uniform period, the reflectivity of Gaussian profile grating with nonuniform period has almost no resonance side lobes at shorter wavelength. And the numerical simulation spectrum is provided.