This study elucidates the influence of the N-related localized states on electron emission properties of a GaAsN quantum well (QW) that is grown by molecular beam epitaxy. The N-related localized states in a GaAsN QW are identified as both optical and electrical electron trap states. Furthermore, exactly how N-related localized states influence the electron emission properties of a GaAsN quantum well is examined. The presence of N-related localized states effectively suppresses the tunneling emission of GaAsN QW electron states, leading to a long electron emission time for the GaAsN QW electron states. Thermal annealing can reduce the number of N-related localized states, resulting in a recovery of the tunneling emission for GaAsN QW electron states. Increasing the annealing temperature can restore the electron emission behavior of GaAsN QW to the typical electron tunneling emission for a high-quality QW.