The design of transverse electromagnetic (TEM) horn antennas has to consider impedance matching between the feeding point and the aperture. To achieve good impedance matching, several typical tapered transmission lines are applied to the taper shape of TEM horns in this study. The numerical estimation of the antenna characteristic of each TEM horn is performed using the finite integration method. An exponential taper is most applicable to the antenna shape among those transmission line tapers. An exponentially tapered TEM horn, however, has problems in maintaining a single main lobe in the radiation pattern. We propose a shortened exponentially tapered TEM horn in which has a simple structure that improves the radiation directivity, and the estimation results show its effectiveness as a broadband antenna.