Based on a staggered double-grating slow wave structure with step-shaped grooves, the expressions of the electromagnetic field in it have been obtained and the formulae of the dispersion equation and coupling impedance have been solved by means of field matching method. As an example, a staggered double-grating slow wave structure for W band TWT application was used to calculate the characteristics of dispersion and coupling impedance using the formulae and CST-MWS code, and analyze the effect of the step dimension variation on the high frequency characteristics. Results show that the theoretical calculations are in good agreement with the CST-MWS code simulations, and the slow wave structure can improve the dispersion characteristics, enhance interaction bandwidth, while keeping a proper coupling impedance and mechanical intensity, which can to some extent compensate for the deficiency in the staggered double-grating slow wave structure with the rectangular-shaped grooves.