Based on coupled mode theory, the reflection properties of the fibre Bragg grating fabricated with phase mask are analysed by transfer matrix method. A new beam path is designed to fabricate fiber gratings and a new short-wavelength self-induced chirping apordized grating with length of 0.015 m is fabricated by Gaussian ultraviolet (UV) beam. Furthermore, a new long-wavelength self-induced chirping grating is obtained by cutting the original fiber grating shorter to 0.007 m and 0.0055 m separately. By contrast with the original grating, the new one has more side lobes on the long-wavelength side of the reflection spectrum and the side-lobes on the short-wavelength side are suppressed. On the basis of analysis of the new self-induced chirping grating, a new type of Gaussian-like apodization function is presented and used to simulate the self-induced chirping of the fiber grating. The theoretical results accord with the experimental results.