  We present the construction of the $D=4$ supergravity action from the minimal
Maxwell superalgebra $s\mathcal{M}_{4}$, which can be derived from the
$\mathfrak{osp}\left( 4|1\right) $ superalgebra by applying the abelian
semigroup expansion procedure. We show that $N=1$, $D=4$ pure supergravity can
be obtained alternatively as the MacDowell-Mansouri like action built from the
curvatures of the Maxwell superalgebra $s\mathcal{M}_{4}$. We extend this
result to all minimal Maxwell superalgebras type $s\mathcal{M}_{m+2}$. The
invariance under supersymmetry transformations is also analized.
