  In this paper, we discuss an artificial intelligence based approach to
constrain the redshift of blazars using combined $\gamma$--ray observations
from the \emph{Fermi} Large Area Telescope (LAT) and ground based atmospheric
Cherenkov telescopes (ACTs) in GeV and \emph{sub} TeV energy regimes
respectively. The spectral measurements in GeV and TeV energy bands show a
redshift dependent spectral break in the $\gamma$--ray spectra of blazars. We
use this observational feature of blazars to constrain their redshift. The
observed spectral information of blazars with known redshifts reported in the
\emph{Fermi} catalogs (3FGL and 1FHL) and TeV catalog are used to train an
Artificial Neural Network (ANN) based algorithm. The training of the ANN
methodology is optimized using \emph{Levenberg - Marquardt} algorithm with
$\gamma$--ray spectral indices and redshifts of 35 well observed blazars as
input and output parameters respectively. After training, we use only observed
spectral indices in GeV and sub TeV regimes for 10 blazars as inputs to predict
their redshifts. The comparison of predicted redshifts by the ANN with the
known redshift suggests that both the values are consistent within $\sim$
18$\%$ uncertainty. The method proposed in the present work would be helpful in
future for constraining or predicting the redshifts of the blazars using only
observational $\gamma$--ray spectral informations obtained from the
\emph{Fermi}-LAT and current generation IACTs as well as from the next
generation Cherenkov Telescope Array (CTA) with improved source statistics.
