An arbitrary multi-way radial power divider/combiner with high-power capacity based on the coaxial waveguide TE01-mode is presented in this paper. The study of the TE01-mode in the coaxial waveguide shows the radial power divider can operate in the base mode with a large diameter, which can allow arbitrary multi-way waveguides to be radially distributed along the circumference of the coaxial waveguide. An equivalent circuit model of the arbitrary multi-way radial power divider is used to analyze its design procedure including the matching section, which can improve the transmission coefficient and isolation between output ports. To verify these, a 4-way and a 20-way radial power divider/combiner with a matching section are designed; the simulation results show that the power capability is >43 kW within 0.5 dB insertion loss for the four-way radial power divider. The average value of isolation between adjacent ports has improved by 11.1 dB after using the periodic matching structure as well as 2.78 dB between opposite ports in the frequency range of 34.08–36.32 GHz. The insertion loss of the 20-way radial power divider is less than 1 dB in the frequency range of 33.4–37.6 GHz, while the return loss is greater than 25 dB.