As a new type all-metal slow-wave structure of the millimeter wave TWT, The helical groove has a lot of advantages: large power handling capability, large sizes, high precision and moderate bandwidth. Of the helical groove structure, the haft-circular helical groove can achieve wider passband than the rectangular helical groove can do. The approximate and much simple matching method of the fields of the half-circular structure is presented in this paper. The more general expressions of the dispersion characteristic and coupling impcdencc, in which the fast-wave modes and slow-wave modes are considered simultaneously, are obtained. It is indicated from the results of the numerical calculation that choosing suitable dimensions of the structure and suppessing the backward wave osillation, this kind of slow-wave structure can operate over 50% “hot” relative bandwidth.