In the work of Qi, Wang & Lu, gamma-ray bursts (GRBs) are used together with an earlier Type Ia supernova (SN Ia) data set to constrain the dark energy equation of state (EOS) in a nearly model-independent way. The improvements made by including GRBs show a slight shift of the dark energy EOS toward w > −1 at redshifts z≳ 0.5. It is interesting that, when we have more SNe Ia, SNe Ia themselves also show the same trend. Motivated by the fact that both SNe Ia and GRBs seem to prefer a dark energy EOS greater than −1 at redshifts z≳ 0.5, we perform a careful investigation of this situation, including more careful treatments of measurement errors of GRBs and cross-checking the results by using different ways of including GRBs. We find that the deviation of dark energy from the cosmological constant at redshifts z≳ 0.5 is large enough that we should pay close attention to it with future observational data. Such a deviation may arise from some biasing systematic errors in the handling of SNe Ia and/or GRBs, or more interestingly from the nature of the dark energy itself.