In this paper, scattering and coupling problems of the directional coupler for the dielectric rectangular waveguides are analyzed by the mode-matching method in the sense of least squares for the fundamental mode incidence. This directional coupler is composed of three parallel dielectric rectangular waveguides cores which are placed at equal space in the dielectric medium. Namely, respective cores are core regions of three respective rectangular waveguides. The central rectangular core among them has periodic groove structures of finite extent on its two surfaces which face each other and other two waveguide cores are perfect. In the central waveguide, the fundamental mode is incident from perfect part toward the periodic structure of this waveguide. The power of the incident mode to the central waveguide is coupled to other two waveguides through periodic groove structure. The coupled mode propagates in the other waveguides to the same or opposite direction for the direction of the incident mode when the Bragg condition is selected appropriately. The method of this paper results in the integral equations of Fredholm type of the second kind for the unknown spectra of scattered fields. The results of the first order approximate solutions of the integral equations are presented in this paper.