Based on the fiber Bragg grating Fabry-Perot (F-P) cavity with identical grating parameters at two ends, using the transfer matrix method and numerical simulation method, the influence of various parameters of fiber Bragg grating F-P cavity on its transmission spectrum features is analyzed, and the delay and dispersion characteristics of the fiber Bragg grating F-P cavity are discussed in detail. Finally, when its cavity length of fiber Bragg grating F-P cavity is changed, the influence on its slow light characteristics is analyzed. The results of this study can be useful for designing Bragg grating F-P cavity, which are also meaningful to actual experiments and applications in using fiber Bragg grating F-P cavity on the slow light and dispersion compensation.