The coherently coupled nonlinear Schrdinger equation is used to study the modulation instability of laser pulses propagating in fiber Bragg gratings with raised cosine apodization function in both anomalous and normal dispersion regimes. The results show that modulation instability is produced in both anomalous and normal dispersion regimes. The obvious regular gain spectra have been produced when the input power reaches a certain value in anomalous dispersion regime. The modulation instability in normal dispersion regime rises from a fixed value to infinite when the input power is in the range that can produce modulation instability. Furthermore, the gain spectra have been restrained by raised cosine apodization function in both dispersion regimes.