A novel slow-wave structure (SWS), the coaxial inverted helical groove structure, is presented and those of its properties used for wide-band traveling-wave tube (TWT) are investigated. The first part of the paper concerns the wave properties of this structure in the case of a vacuum. The influence of the geometrical dimensions on dispersion characteristics and interaction impedance are investigated. The theoretical results reveal a very weak dispersion for the fundamental wave in the structure. The negative dispersion can be realized by a suitable selection of the structural parameters. The interaction impedance of the fundamental wave is about 10 Ω. The interaction impedance of the -1 space harmonic wave is much lower than that of the fundamental wave. Thus, the risk of backward wave oscillation is reduced. The software high frequency structure simulator (HFSS) is also used to calculate the dispersion property of the SWS. The simulation results from HFSS and the theoretical results agree well, which supports the theory. In the second part, a self-consistent linear theory of a coaxial inverted helical groove TWT is presented. The typical small signal gain per period is about 0.5 dB and the 3-dB small-signal gain bandwidth can exceed 25% with a 33-dB gain of tube.