In this study, AlGaN/GaN light-emitting HEMTs (LE-HEMT) with a single quantum well inserted in different locations in the epitaxy layers are fabricated and analyzed. For both structures, light-emitting originated from electrons in the 2DEG and holes from the p-GaN for radiative recombination is located in the quantum well. To investigate the importance of the location of single quantum well, optical characteristics are compared by simulation and experimental results. The experimental results show that the main light-emitting wavelength is shifted from 365 nm in the UV range to 525 nm in the visible range when the radiative recombination is confined in the quantum well and dominates among other mechanisms. Epi B, which has a quantum well above the AlGaN barrier layer in contrast to Epi A which has a quantum well underneath the barrier, shows better intensity and uniformity in light-emitting. According to the simulation results showing the radiative distribution and electron concentrations for both structures, the lower quantum efficiency is due to the diverse current paths in Epi A. On the other hand, Epi B shows better quantum confinement and therefore better luminescence in the same bias condition, which is consistent with experimental observations. These findings are critical for advancing the performance of LE-HEMTs.