  A shift-symmetric Galileon model in presence of spacetime torsion has been
constructed for the first time. This has been realized by localizing (or,
gauging) the Galileon symmetry in flat spacetime in an appropriate manner. We
have applied the above model to study the evolution of the universe at a
cosmological scale. Interestingly, for a wide class of torsional structures we
have shown that the model leads to late time cosmic acceleration. Furthermore,
as torsion vanishes, our model reproduces the standard results.
