The distribution of the TEM wave in a coaxial transmission line with circular - inner - conductor and regular - hexagon - outer - conductor is obtained by using numerical conformal mapping. The map of structure of electromagnetic field is plotted by using the software MATLAB and HFSS，and its characteristic impedance is calculated. Furthermore，its characteristic impedance is calculated. This research result has certain reference value to calculation of the decay constant of the transmission line，realization of its power capability，consideration of its power coupling and design of the related active device.