We grew high quality In-rich InGaN/GaN single quantum well (SQW) structures by metal-organic chemical vapor deposition using growth interruption and obtained a sharp photoluminescence peak in near-ultraviolet (UV) region. During In-rich InGaN well layer growth, only TMIn and ammonia were supplied, however, atomic interdiffusion as well as defect generation occurred to relieve large lattice mismatch over 10% between InN and GaN. From medium-energy ion scattering measurement and subsequent fitting of the spectrum, we could find that the InGaN well layer was In-rich and it has 60-70% indium content. We also found the compositional grading of indium at top and bottom InGaN/GaN interfaces. The Fourier series method was used to calculate the energy levels and envelope functions in In-rich InGaN/GaN SQW with compositional grading and we could quantitatively explain the near-UV emission observed from the SQW.