TEM Horn is an ultra-wide-band antenna, which is usually employed in the analysis of frequency domain up to the present. A new concept is presented with wave mode theory. According to this concept, the impedance of antenna aperture cannot be regarded as the wave impedance in vacuum, but is connected with antenna size and flare angle. Because of the time sequence, the reflection is only connected with local structure. A TEM horn antenna is designed and fabricated. The experiment results show that its wave fidelity and impedance performance are excellent, so it is very valuable for the study of time-domain antenna.