  By employing a simple semi-analytical star formation model where the
formation rates of Population (Pop) I/II and III stars can be calculated,
respectively, we account for the number distribution of gamma-ray bursts (GRBs)
with high pseudo-redshifts that was derived from an empirical
luminosity-indictor relationship. It is suggested that a considerable number of
Pop III GRBs could exist in the present sample of Swift GRBs. By further
combining the implication for the star formation history from the optical depth
of the CMB photons, it is also suggested that only a very small fraction 0.6%
of Pop III GRBs could have triggered the Swift BAT. These results could provide
an useful basis for estimating future detectability of Pop III stars and their
produced transient phenomena.
