We present the global distributions of trapped He (4.8-37 MeV) fluxes in the low altitude region under quiet-time conditions (|Dst| < 30 nT) of geomagnetic activity. Observations were obtained by the OHZORA satellite during 1984-1987 in the altitude of350-850km. We have compared the global distributions of He fluxes with those for trapped electrons and protons at the same altitudes. Auroral zones observed from energetic He are not so prominent as compared with those from electron and proton fluxes. It is found that the anomalous distributions of He fluxes are localized at the South Atlantic Anomaly, while the anomalous distributions of electron and proton fluxes are clearly seen to extend from South Atlantic region to Southern Anomaly. Further, the L-distributions of trapped He fluxes are also examined during quiet-time conditions. It is found that the distributions for lower energies (4.8-13MeV) have two peaks at L =~ 1.4 and ~ 2.7, while the distribution for higher energies (13-37 MeV) has a single peak at L ~ 1.5 and does not have the peak at L =~ 2.7.