  Recent studies suggest that Swift gamma-ray bursts (GRBs) may not trace an
ordinary star formation history. Here we show that the GRB rate turns out to be
consistent with the star formation history with an evolving stellar initial
mass function (IMF). We first show that the latest Swift sample of GRBs reveals
an increasing evolution in the GRB rate relative to the ordinary star formation
rate at high redshifts. We then assume only massive stars with masses greater
than the critical value to produce GRBs, and use an evolving stellar IMF
suggested by Dav\'{e} (2010) to fit the latest GRB redshift distribution. This
evolving IMF would increase the relative number of massive stars, which could
lead to more GRB explosions at high redshifts. We find that the evolving IMF
can well reproduce the observed redshift distribution of Swift GRBs.
