The polarization-induced electric field in the III-nitride UV light-emitting diode (LED) allows for significant flexibility in device design to address the electron overflow and hole injection issues. The conventional AlGaN-based UV LED with the PIN structure suffers from insufficient carriers especially hole concentration due to the large valence band barrier for hole injection and p-type doping challenge. Our systematic study reveals that the inverse design of the n-type and p-type layer shall build an opposite polarization-induced field to suppress electron overflow as well as simultaneously enhance hole injection. To design this p-side down UV LED and improve the hole injection, we adopt the n-AlGaN/i-InGaN/p-AlGaN buried tunneling junction (BTJ) instead of the bottom p-layer. The tunneling probability and output power of the LED are further investigated by optimizing the composition and thickness of the InGaN layer. Simulation results show that the optimized 3 nm In0.3Ga0.7N tunneling layer could lead to several orders of magnitude enhancement for LED output power. This study is significant for the pursuit of highly efficient UV LEDs.