On the basis of coupled mode theory the linear dispersion relation in an infinite one dimensional periodic structure is given and then a class of slow Bragg soliton like solutions is found by introducing the nonlinearity. It is shown that an increase of intensity will lead to strengthen the effect of group velocity dispersion. Because of the nonlinearity, the width of stop band structure decreases, and the pulse attains an instantaneous frequency which depends on the detuned parameter, velocity, intensity and nonlinear coefficient.