  We determine the metallicity distribution function (MDF) of the Galactic halo
based on metal-poor main-sequence turnoff-stars (MSTO) which were selected from
the Hamburg/ESO objective-prism survey (HES) database. Corresponding follow-up
moderateresolution observations (R ~ 2000) of some 682 stars (among which 617
were accepted program stars) were carried out with the 2.3m telescope at the
Siding Spring Observatory (SSO). Corrections for the survey volume covered by
the sample stars were quantitatively estimated and applied to the observed MDF.
The corrections are quite small, when compared with those for a previously
studied sample of metal-poor giants. The corrected observational MDF of the
turnoff sample was then compared with that of the giants, as well as with a
number of theoretical predictions of Galactic chemical evolution, including the
mass-loss modified Simple Model. Although the survey-volume corrected MDFs of
the metal-poor turnoff and the halo giants notably differ in the region of
[Fe/H] > -2.0, below [Fe/H] ~ -2.0, (the region we scientifically focus on
most) both MDFs show a sharp drop at [Fe/H] ~ -3.6 and present rather similar
distributions in the low-metallicity tail. Theoretical models can fit some
parts of the observed MDF, but none is found to simultaneously reproduce the
peak as well as the features in the metal-poor region with [Fe/H] between -2.0
to -3.6. Among the tested models only the GAMETE model, when normalized to the
tail of the observed MDF below [Fe/H] ~ -3.0, and with Z_{cr} =
10^{-3.4}Z_{\odot}, is able to predict the sharp drop at [Fe/H] ~ -3.6.
