The characteristics of a three‐mode coupling in a dielectric slab waveguide attached doubly periodic surface corrugations are investigated. The coupled‐mode equations governing the first‐order Bragg interactions of three TE modes are systematically derived with the help of perturbation procedure. For the case where the waveguide is symmetric and the three TE modes are lowest even modes, the coupled‐mode equations are solved to obtain the reflection and transmission characteristics of the periodic waveguide of finite length. The results are compared with those of the two related two‐mode couplings in a dielectric slab waveguide with a singly periodic surface corrugation.