In this work, III-nitride based ~370 nm UVA light-emitting diodes (LEDs) grown on Si substrates are demonstrated. We also reveal the impact of the AlN composition in the AlGaN quantum barrier on the carrier injection for the studied LEDs. We find that, by properly increasing the AlN composition, both the electron and hole concentrations in the multiple quantum wells (MQWs) are enhanced. We attribute the increased electron concentration to the better electron confinement within the MQW region when increasing the AlN composition for the AlGaN barrier. The improved hole concentration in the MQW region is ascribed to the reduced hole blocking effect by the p-type electron blocking layer (p-EBL). This is enabled by the reduced density of the polarization-induced positive charges at the AlGaN last quantum barrier (LB)/p-EBL interface, which correspondingly suppresses the hole depletion at the AlGaN LB/p-EBL interface and decreases the valence band barrier height for the p-EBL. As a result, the optical power is improved.