Based on nine BATSE GRBs with known redshifts, we found that the maximum spectral lag of all the pulses in a gamma-ray burst (GRB) appears to be anti-correlated with the redshift of the burst. In order to confirm this finding, we analyzed 10 GRBs detected by HETE-2 with known redshifts and found a similar relation. Using the relation, we estimated the redshifts of 878 long GRBs in the BATSE catalog, then we investigated the distributions of the redshifts and 869 E_iso of these GRBs. The distribution of the estimated redshifts is concentrated at z = 1.4 and the distribution of E_iso peaks at 10^52.5 erg. The underlying physics of the correlation is unclear at present.