  We investigate in this paper the structures of neutron stars under the strong
magnetic field in the framework of $f(T)$ gravity where $T$ denotes the scalar
torsion. The TOV equations in this theory of gravity have been considered and
numerical resolution of these equations has been performed within perturbative
approach taking into account the equation of state of neutron dense matter in
magnetic field. We simplify the problem by considering the very strong magnetic
field which affects considerably the dense matter; and for quadratic and cubic
corrections to Teleparallel term, one finds that the mass of neutron stars can
increase for different values of the perturbation parameter. The deviation from
Teleparallel for different values of magnetic field is found out and this
feature is very appreciable in the case of cubic correction. Our results are
related to the hadronic particles description with very small hyperon
contributions and the mass-radius evolution is consistency with the
observational data.
