Traveling wave tube (TWT) is an attractive solution for wideband and high-power sources or amplifiers in the terahertz (THz) band. In this article, a novel slow-wave structure (SWS) for TWT, named double tunnel sine waveguide (DTSW), which is based on sine waveguide (SW), is proposed. The following key technologies are adopted: 1) the rectangular holes, at which the operating mode is cutoff, are alternately opened on the sine-shaped ridges to form two electron beam tunnels and 2) the lower surface of rectangular holes is flush with the top of sine-shaped ridges. Compared with the SW-SWS, DTSW-SWS has the wider operating band and higher interaction impedance under the condition that the phase velocity of the two SWSs is at the same level. In addition, DTSW-SWS is simple in structure and easy to fabricate. The particle-in-cell simulation results reveal that DTSW-TWT has an output power of more than 202 W in the frequency range of 202-255 GHz with the maximum power of ~405 W and electron efficiency of ~9.8% at 215 GHz, under the operating voltage of 23 kV and beam current of 180 mA. Therefore, the DTSW should be considered as a promising SWS for the high-power and wideband THz traveling wave amplifier.