The development of a neutron detector for real-time measurements in an intense neutron field is desired. We are developing a quartz optical-fiber-based neutron detector as a real-time neutron monitor. Thus far, Eu:LiCaAlF6 crystals and LiF/Eu:CaF2 eutectics were used as the scintillators of the quartz optical-fiber-based neutron detectors. These scintillators have high light yields, but relatively long decay time constants, which are limitation factors of the dynamic range of optical-fiber-based neutron detectors. In this paper, we applied a small Li-glass scintillator to a quartz optical-fiber-based neutron detector using an optical fiber with high numerical aperture (NA) and a UV-curable resin with high transmittance. The fabricated detector showed a clear peak corresponding to neutron events in the pulse height distribution. The radiation resistance was evaluated and no deterioration was observed up to 2×1012 n/cm2. The detector output linearity was confirmed up to 450 kcps, which was about ten times larger than that of the detector using the conventional Eu:LiCaAlF6 or LiF/Eu:CaF2 scintillator.