Abstract: In order to analyze the rectangular waveguide grating which is a typical slow wave structure, the dispersion relation was obtained by the field-matching method. The coupling impedance was subsequently obtained from the relevant equations. The higher orders were retained as an infinite sum of standing eigen-waves to deal with the fields inside the grooves. Computations and analysis were done for two typical structures of the rectangular waveguide grating, the shallow grating and the deep grating, and reasonable results were obtained. The results show that the deeper the groove is, the stronger the dispersion is and the narrower the pass-band is. The coupling impedance increases significantly. The operating point moves toward the forward wave zone, it is fit for the slow wave structure of an