Based on the finite element method and transmission matrix method, the reflection spectrum of the grapefruit-type structure photonic crystal fiber chirped grating is analyzed theoretically. Compared with the results of simulation and experimental, it is seen that the method is feasible. The results show that the chirped grating has several reflection peaks. Moreover, the influences of the chirp coefficient and refractive indexes modulation on the resonant bandwidth and reflectivity are simulated. It is found that with the increase of the chirp coefficient and refractive indexes modulation, the reflection spectrum is changed regularly. When the chirp coefficient increases to a certain extent, the four reflection peaks can be connected together to form a large reflection bandwidth. At the same time, the delay characteristics of fundamental mode are studied. It can be seen that photonic crystal fiber chirped grating has a relatively smooth delay curve, so it can be used for dispersion compensation.