A folded diamond shaped waveguide slow wave structure （SWS） is proposed and investigated in this paper. Compared with the conventional folded rectangular waveguide SWS， the folded diamond shaped waveguide SWS is larger with the same frequency band， and the bandwidth is broader with the same dimension. The input-output waveguide transition structure and attenuator appropriate for this kind of SWS are put forward. Based on the proposed folded diamond shaped waveguide （FDSWG） SWS， we designed the whole SWS for a 340 GHz traveling wave tube （TWT）， in which the negative phase-velocity tapering technique is adopted to improve the gain. The particle-in-cell results show that its output power and gain at 343 GHz can reach 8 w and 33 dB， respectively. Its 3-dB bandwidth is from 330 GHz to 348 GHz， with a circular electron beam of 15.3 kV and 35 mA.