Based on multipole method and coupled-mode theory,the transmission spectrum of a typical hexagonal lattice photonic crystal fiber Bragg grating is analyzed and simulated by Matlab. The differences between conventional fiber grating and photonic crystal fiber grating on their transmission spectrum and delay characteristics are compared,and derived qualitatively. The apodization characters of this fiber grating are also researched,the optimal apodization function and corresponding transimission spectrum are obtained. It is found that the effective refractive indexes of core mode decline as wavelength rising,compared with the conventional fiber grating,photonic crystal fiber grating has the shorter resonant wavelength,when it is added chirp,10 cm photonic crystal fiber grating can provide 1200 ps linear delay.