Based on the coupled mode theory and the FORTRAN software, study are carried out for the frequency response in a coaxial Bragg reflector with gradual change ripples. Results show that the characteristics of frequency response in the positive gradual change or the negative gradual change ripples coaxial Bragg reflector are the agreement, and the bandwidth of the coaxial Bragg reflector with gradual change ripples can be expanded as the gradual angle augmenting when the incident mode is Single-mode and lower frequency; When the incident mode is Coupled-mode and higher frequency, the bandwidth of the operating mode and the spurious mode also all can be expanded as the gradual angle augmenting, but the negative gradual change ripples can get higher frequency than the positive gradual change when the gradual angles are same; and the residual side-lobes of the frequency response also can be effectively suppressed. These characteristics of a gradual change ripples coaxial Bragg reflector are favorable to improvement of the performance as a reflector or a filter in its applications.