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Let $D=(V,A)$ be a digraphs without isolated vertices. The first Zagreb indexof 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 thevertex $u$. In this paper, we give the maximal values and maximal digraphs offirst Zagreb index over the set of all orientations of unicyclic graphs with$n$ vertices and matching number $m$ $(2\leq m\leq \lfloor\frac{n}{2}\rfloor)$.

Maximum first Zagreb index of orientations of unicyclic graphs with given matching number