Radio telescopes usually conduct continuous observation across a wide frequency range, but traditional phased array antenna designs struggle to meet the requirements of both wide band and large scanning volume. The development of tightly coupled antennas offers a novel approach for addressing these challenges. Accordingly, a wideband dual-polarized Vivaldi phased array feed has been designed. Firstly, a theoretical analysis of the tightly coupled principle is conducted, incorporating Wheeler's concept of continuous current and equivalent circuit. It reveals that the strong coupling between the antenna elements effectively expands the operational bandwidth of the Vivaldi phased array. Based on this, a wideband Vivaldi phased array feed composed of 8×9 Vivaldi antenna elements with a operational frequency ranging from 2 to 8 GHz is designed. Furthermore, the phased array enables $45^\circ$ scanning characteristics in both E-plane and H-plane. Finally, a prototype of the phased array is fabricated and measured. The measurement results are in good agreement with the simulated ones.