Boron neutron capture therapy (BNCT) is one of the radiation therapies using neutrons. In BNCT, neutron monitoring is essential to ensure safety and evaluate the effect of treatments. As a neutron monitor for BNCT, we are developing an optical-fiber-based neutron detector using a small Li glass scintillator. This type of detector shows a clear neutron peak in the pulse height spectrum and has a high counting-rate capability owing to its short decay time. However, the sensitivity of the detector is uncontrollable owing to its random scintillator shape. In this study, we propose a Li glass transparent composite scintillator, in which Li glass grains and UV-curable resin are mixed, to realize a small and shape-controlled scintillator. We first fabricated the Li glass transparent composite scintillator and then experimentally confirmed that its response showed a clear neutron peak. We also fabricated an optical-fiber-based neutron detector using the Li glass transparent composite scintillator. The scintillator was formed into a hemispherical shape at the tip of an optical fiber. We confirmed the response of the optical-fiber-based detector, which showed a clear neutron peak. The experimentally evaluated sensitivity of the fabricated optical-fiber-based detector roughly agreed with the sensitivity estimated from its shape and size. Therefore, we conclude that the sensitivity of the optical-fiber-based neutron detector can be roughly controlled by using the Li glass transparent composite scintillator.