With the framework of the coupled modes theory,transmission of the Bragg solitons and interaction of the Bragg solitons are simulated with the finite-difference scheme in raised cosine apodized-fiber bragg gratings.According to the numerical results,the raised cosine apodized-gratings lead the stable transmission of Bragg solitons under the condition of suitable choice of input power and the initial width of pulse.And interactions of two solitons rely on their relative phase and amplitude.The mutual attraction,rejection and energy exchange happened between two solitons with the different parameters of relative phase and amplitude.