  The behavior of the dark energy equation of state (EOS) is crucial in
distinguishing different cosmological models. With a model independent
approach, we constrain the possible evolution of the dark energy EOS. Gamma-ray
bursts (GRBs) of redshifts up to $z>6$ are used, in addition to type Ia
supernovae (SNe Ia). We separate the redshifts into 4 bins and assume a
constant EOS parameter for dark energy in each bin. The EOS parameters are
decorrelated by diagonalizing the covariance matrix. And the evolution of dark
energy is estimated out of the uncorrelated EOS parameters. By including GRB
luminosity data, we significantly reduce the confidence interval of the
uncorrelated EOS parameter whose contribution mostly comes from the redshift
bin of $0.5<z<1.8$. At high redshift where we only have GRBs, the constraints
on the dark energy EOS are still very weak. However, we can see an obvious cut
at about zero in the probability plot of the EOS parameter, from which we can
infer that the ratio of dark energy to matter most probably continues to
decrease beyond redshift 1.8. We carried out analyses with and without
including the latest BAO measurements, which themselves favor a dark energy EOS
of $w<-1$. If they are included, the results show some evidence of an evolving
dark energy EOS. If not included, however, the results are consistent with the
cosmological constant within $1 \sigma$ for redshift $0<z \lesssim 0.5$ and $2
\sigma$ for $0.5 \lesssim z<1.8$.
