A 340 GHz Backward Wave Tube(BWT) based on Staggered Double Rectangular Waveguide Structure(SDRWS) is studied in detail by computer simulation. Firstly, an electron gun and a permanent magnet focus system are calculated, the results shows that beams with 14 kV-17 kV of voltage, 43.4 mA of current and 18-21 kV of voltage, 56.1 mA of current are produced and maintained, the maximum radius of the beam is smaller than 0.08 mm, and the maximum radius variance of the beam reaches 0.034 mm. Secondly, combining those beams with SDRWS, the interaction in the BWT based on SDRWS is calculated, the results shows that the working frequencies of the BWT cover 326-352.6 GHz when the beam voltage is tuned within 14-21 kV and the output powers of the BWT are larger than 2 W. In the simulations, the radius of the SDRWS is set to be a relatively big value of 0.09 mm, signifying that the manufacturing of the BWT is relatively easy.