This paper presents a theory on accurately analysing the dispersion relation and the interaction impedance of electromagnetic waves propagating through a helical groove waveguide with arbitrary groove shape, in which the complex groove profile is synthesized by a series of rectangular steps. By introducing the influence of high-order evanescent modes on the connection of any two neighbouring steps by an equivalent susceptance under a modified admittance matching condition, the assumption of the neglecting discontinuity capacitance in previously published analysis is avoided, and the accurate dispersion equation is obtained by means of a combination of field-matching method and admittancematching technique. The validity of this theory is proved by comparison between the measurements and the numerical calculations for two kinds of helical groove waveguides with different groove shapes.