A novel slow-wave structure called V-shape folded rectangular groove waveguide is proposed. This structure evolves from a conventional rectangular groove waveguide bending the groove with V-shape along its longitudinal direction, and the gap between metal plates forms a sheet electron beam channel naturally. Compared with the traditional U-shape structure, it can increase the interaction area without changing good high-frequency properties, which can adopt the sheet electron beam with a larger area to acquire more output power. In this paper, the high-frequency properties of this structure are analyzed, the interaction circuit for the V-band TWT is designed and the PIC simulation is performed to predict the operating characteristics. From our calculations, this tube can produce average saturation output power over 1000 Watts in a frequency range from 58 GHz to 64 GHz when the cathode voltage and beam current are set to be 12.8 kV and 600 mA respectively. The corresponding saturation gain and electron efficiency can reach over 33 dB and 13.2% respectively.