The step-loaded rectangular waveguide grating slow-wave system, a new type slow-wave structure for mm-millimeter TWT, was presented in this study. And the dispersion equation and coupling impedance of this circuit were obtained by means of the approximate field matching theory, in which the high order terms of the field expansion in the groove region were considered, and the jump conditions at the interface of two neighboring steps and the matching conditions at the interface between the loaded region and the interaction region were employed. The high-frequency characteristics of the fundamental wave were discussed and the influence of various circuit parameters on high-frequency characteristics was also investigated. The results of the numerical calculation show that it is very useful for improving the high-frequency characteristics by loading the steps. The specific design-parameters can be selected according to the different needs. The present analysis will be helpful for further study and design of this kind RF system.