We have designed a backward wave oscillator (BWO) using a staggered double grating (SDG) slow-wave structure (SWS) and a sheet beam generated by a pseudo-spark cathode. The CST simulation results for the high-frequency characteristics of the SWS are analyzed, and the operating oscillation frequency point is found to be 365.13 GHz at 35000 V. The BWO model is created and the power performance is obtained with particle-in-cell (PIC) simulation. The frequency is 365.93 GHz at 35000 V, which is 0.16% higher than the predicted one by the Brillouin diagram. In the voltage range from 33500 V to 37000 V, a bandwidth of 2.38 GHz with power of over 200 W is achieved. The power could be over 1000 W from 365.5 GHz to 365.5 GHz, showing that significant output power is obtained.