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We investigate the mass distribution of long gamma-ray burst (GRB) hostgalaxies and the redshift distribution of long GRBs by considering that longGRBs occur in low-metallicity environments. We calculate the upper limit on thestellar mass of a galaxy which can produce long GRBs by utilizing themass-metallicity (M-Z) relation of galaxies. After comparing with the observedGRB host galaxies masses, we find that the observed GRB host galaxy masses canfit the predicted masses well if GRBs occur in low-metallicity$12+\log\rm(O/H)_{\rm KK04}<8.7$. GRB host galaxies have low metallicity, lowmass, and high star formation rate compared with galaxies of seventh datarelease of the Sloan Digital Sky Survey. We also study the cumulative redshiftdistribution of the latest \emph{Swift} long GRBs by adding dark GRBs and 10new GRBs redshifts from TOUGH survey. The observed discrepancy between the GRBrate and the star formation history can be reconciled by considering that GRBstend to occur in low-metallicity galaxies with $12+\log\rm(O/H)_{\rmKK04}<8.7$. We conclude that the metallicity cutoff that can produce long GRBsis about $12+\log\rm(O/H)_{\rm KK04}<8.7$ from the host mass distribution andredshift distribution.

Long GRBs are metallicity-biased tracers of star formation: evidence from host galaxies and redshift distribution