  Let $D=(V,A)$ be a digraphs without isolated vertices. The first Zagreb index
of a digraph $D$ defined as a summation over all arcs,
$M_1(D)=\frac{1}{2}\sum\limits_{uv\in A}(d^{+}_{u}+d^{-}_v)$, where
$d^{+}_u$(resp. $d^{-}_u$) denotes the out-degree (resp. in-degree) of the
vertex $u$. In this paper, we give the maximal values and maximal digraphs of
first Zagreb index over the set of all orientations of unicyclic graphs with
$n$ vertices and matching number $m$ $(2\leq m\leq \lfloor
\frac{n}{2}\rfloor)$.
