  We explore the gamma-ray bursts' (GRBs') contributions in constraining the
dark energy equation of state (EOS) at high ($1.8 < z < 7$) and at middle
redshifts ($0.5 < z < 1.8$) and estimate how many GRBs are needed to get
substantial constraints at high redshifts. We estimate the constraints with
mock GRBs and mock type Ia supernovae (SNe Ia) for comparisons. When
constraining the dark energy EOS in a certain redshift range, we allow the dark
energy EOS parameter to vary only in that redshift bin and fix EOS parameters
elsewhere to -1. We find that it is difficult to constrain the dark energy EOS
beyond the redshifts of SNe Ia with GRBs unless some new luminosity relations
for GRBs with smaller scatters are discovered. However, at middle redshifts,
GRBs have comparable contributions with SNe Ia in constraining the dark energy
EOS.
