Very wideband apertures are needed in positioning, sensing, spectrum monitoring, and modern spread spectrum, e.g., frequency hopping systems. Vivaldi antennas are one of the prominent choices for the aforementioned systems due to their natural wideband characteristics. Furthermore, tightly-coupled antenna arrays have been researched in the recent years to extend the lower band edge of compact arrays by taking advantage of the strong mutual coupling between the elements especially with dipole elements, but not with dual-polarized Vivaldi antennas. This paper presents a novel tightly-coupled dual-polarized antipodal Vivaldi antenna (TC-AVA) with -6 dB impedance bandwidth of 3 to 20 GHz. The tight coupling by overlapping the Vivaldi leaves is shown to extend the lower band edge from 3.75 to 3 GHz and 2.75 GHz, an improvement of 20% to 25% for both polarizations, compared with an isolated antipodal Vivaldi element.