According to the band-pass filtering characteristics of chirped fiber Bragg gratings, a fiber core/cladding composite chirped fiber Bragg gratings filter is designed. Firstly, the spectral characteristics are simulated and analyzed based on the fiber coupling mode, transmission matrix theory and coordinate transformation method, and the double band-pass filtering characteristics of the grating are verified. Then, the spectra of the fiber core/cladding composite structures with periods of 536, 537 and 538nm, grating lengths of 8, 10 and 12mm, refractive index modulation depth of 0.0002, 0.0003 and 0.0004, chirp coefficients of 0.05, 0.10 and 0.15nm/cm were simulated. The half-peak width increases with the grating length, refractive index modulation depth and chirp coefficient. The peak reflectance increases with the increase of refractive index modulation depth and decreases with the increase of chirp coefficient. It is proved that this grating has double band-pass filtering characteristics and its amplitude bandwidth is adjustable.