Context : Aims : 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 . Methods : 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 . Results : 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 . Conclusions :