We have studied the growth of GaInNAs/GaAs quantum well (QW) by molecular beam epitaxy using a DC plasma as the N sourer. The N concentration was independent of the As pressure and the In concentration, but inversely proportional to the growth rate. It was almost independent of T, over the range of 400-500 degreesC, but dropped rapidly when T-g exceeded 500 degreesC. Thermally-activated N surface segregation is considered to account for the strong falloff of the N concentration. As increasing N concentration, the steep absorption edge of the photovoltage spectra of GaInNAs/GaAs QW became gentle, the full-width at half-maximum of the photoluminescence (PL) peal; increased rapidly, and a so-called S-shaped temperature dependence of PL peak energy showed up. All these were attributed to the increasing localized state as N concentration. Ion-induced damage was one of the origins of the localized state. A rapid thermal annealing procedure could effectively remote the localized state.