Neutral Helium multiplets, HeI*3189,3889,10830 are very useful diagnostics to the geometry and physical conditions of the absorbing gas in quasars. So far only a handful of HeI* detections have been reported. Using a newly developed method, we detected HeI*3889 absorption line in 101 sources of a well-defined sample of 285 MgII BAL quasars selected from the SDSS DR5. This has increased the number of HeI* BAL quasars by more than one order of magnitude. We further detected HeI*3189 in 50% (52/101) quasars in the sample. The detection fraction of HeI* BALs in MgII BAL quasars is about 35% as a whole, and increases dramatically with increasing spectral signal-to-noise ratios, from 18% at S/N = 35. This suggests that HeI* BALs could be detected in most MgII LoBAL quasars, provided spectra S/N is high enough. Such a surprisingly high HeI* BAL fraction is actually predicted from photo-ionization calculations based on a simple BAL model. The result indicates that HeI* absorption lines can be used to search for BAL quasars at low-z, which cannot be identified by ground-based optical spectroscopic survey with commonly seen UV absorption lines. Using HeI*3889, we discovered 19 BAL quasars at z