  Let $G$ be a connected graph. The revised edge Szeged index of $G$ is defined
as $Sz^{\ast}_{e}(G)=\sum\limits_{e=uv\in
E(G)}(m_{u}(e|G)+\frac{m_{0}(e|G)}{2})(m_{v}(e|G)+\frac{m_{0}(e|G)}{2})$, where
$m_{u}(e|G)$ (resp., $m_{v}(e|G)$) is the number of edges whose distance to
vertex $u$ (resp., $v$) is smaller than the distance to vertex $v$ (resp.,
$u$), and $m_{0}(e|G)$ is the number of edges equidistant from both ends of
$e$, respectively. In this paper, the graphs with minimum revised edge Szeged
index among all the unicyclic graphs with given diameter are characterized.
