  It is known that the soft tail of the gamma-ray bursts' spectra show excesses
from the exact power-law dependence. In this article we show that this
departure can be detected in the peak flux ratios of different BATSE DISCSC
energy channels. This effect allows to estimate the redshift of the bright long
gamma-ray bursts in the BATSE Catalog. A verification of these redshifts is
obtained for the 8 GRB which have both BATSE DISCSC data and measured optical
spectroscopic redshifts. There is good correlation between the measured and
esti redshifts, and the average error is $\Delta z \approx 0.33$. The method is
similar to the photometric redshift estimation of galaxies in the optical
range, hence it can be called as "gamma photometric redshift estimation". The
estimated redshifts for the long bright gamma-ray bursts are up to $z \simeq
4$. For the the faint long bursts - which should be up to $z \simeq 20$ - the
redshifts cannot be determined unambiguously with this method.
