It is attractive to use sheet beam vacuum devices to generate high frequency, high-power microwave radiation. In this paper, we present the numerical and experimental studies of a high-power Ka-band sheet electron beam backward wave oscillator (BWO), in which the double-grating rectangular waveguide is used as the slow wave structure (SWS) for its thermal and mechanical robustness. The fundamental mode of this kind of SWS is an antisymmetric mode which has an antisymmetric longitudinal field distribution and will nonsynchronously interact with the electron beam on two sides of the electron channel along the vertical direction. We put forward a method to overcome this trouble in this paper. To drive this BWO, a high-power sheet beam is used with a cross section of 30 mm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="TeX">$\times\,$ </tex-math></inline-formula> 1 mm. A thin graphite cathode is used for its superiority in producing a high current, high-quality electron beam. For an experimental electron beam of 141 kV and 1668 A, the output power of over 46.8 MW at 31.68 GHz is obtained, which corresponds to a beam–wave interaction efficiency of 19.9%. Compared with the conventional hollow beam BWO and the single-grating rectangular waveguide sheet beam BWO, the double-grating sheet beam BWOs efficiency is higher, which indicates that the double-grating sheet beam device is promising for producing millimeter wave radiation with high power and high efficiency.