In this work, a novel metamaterial lens (metalens) is designed and optimized to improve the radiation performance of an antipodal Vivaldi antenna for wideband applications. The metalens is integrated into the antenna substrate, and placed close to the tapered slot in the end-fire direction, allowing the preservation of the lightweight and compactness of the antenna. The prototype has been fabricated and characterized, demonstrating good agreement with the simulations. The insertion of the metalens allows, with respect to the pristine Vivaldi, a measured maximum gain of $G_{max}=14.2 \mathrm{d}\mathrm{B}$, increased by about $\Delta G_{max}=4.8 \mathrm{d}\mathrm{B};$ an operating bandwidth of $f=3÷14.7 \mathrm{G}\mathrm{H}\mathrm{z}$, increased by $\Delta f=1.2 \mathrm{G}\mathrm{H}\mathrm{z}$; and a radiation pattern with a maximum reduction in half-power beamwidth of $\Delta HPB{W}_{max}=31.3°$, more symmetrical in the E and H planes.