  For a closed surface $S$, its Torelli group $\mathcal{I}(S)$ is the subgroup
of the mapping class group of $S$ consisting of elements acting trivially on
$H_1(S;\mathbb{Z})$. When $S$ is orientable, a generating set for
$\mathcal{I}(S)$ is known. In this paper, we give a normal generating set of
$\mathcal{I}(N_g)$ for $g\geq4$, where $N_g$ is a genus-$g$ non-orientable
closed surface.
