  In the present work, we have discussed the four dimensional spherically
symmetric steller system in the framework of modified $f(T)$ gravity theory
with electro-magnetic field. The field equations have been written for two
cases, either $T'=0$ or $f_{TT}=0$. Next we have discussed the charged
gravastar model which has three regions: interior region, shell region and
exterior region. In the interior region, we have found the solutions of all
physical quantities like density, pressure, electro-magnetic field and also the
metric coefficients for both the cases. For $T'=0$, gravastar cannot form but
it forms only for the case $f_{TT}=0$. In the exterior region, we have obtained
the exterior solution for vacuum model. In the shell region, we have assumed
that the interior and exterior regions join together at a place, so the
intermediate region must be thin shell with the approximation $h\ll 1$. Under
this approximation, we have found the analytical solutions. The proper length
of the thin shell, entropy and energy content inside the thin shell have been
found and they are directly proportional to the proper thickness of the shell
$\epsilon$ under the approximation ($\epsilon\ll 1$). According to the
Darmois-Israel formalism, we have studied the matching between the surfaces of
interior and exterior regions of the gravastar. The energy density, pressure,
equation of state parameter on the surface and mass of the thin shell have been
obtained.
