The band structure and the transmission properties of the fiber Bragg grating are investigated in the scope of the photonic crystal. The plane wave expansion method is used to analyze the photonic crystal, and is translated into the scope of the fiber Bragg gratings. The optical properties of the fiber Bragg grating are obtained after plenty of numerical computations. It shows that there are many reflection peak-value frequencies, which are integer times to the fundamental frequency. Every peak-value frequency reflects a photonic band gap, its center frequency and band width are related with the grating parameters, such as the grating length, the index modulation depth, and the duty ratio of the material with high dielectric constant. All results are same as those from the conventional coupling mode theory.