On the basis of coupled-mode theory we find a class of solitary solutions for the electromagnetic wave propagating in an infinite one-dimensional periodic structure with an intensity-dependent refractive index. We show that the amplitude of the solitary wave is dependent of the incident frequency and the pulse width. In the Bragg resonance limit, the solitary wave can be simplified to a soliton-like solution which was named as “gap soliton” or “slow Bragg soliton”.