  A {\it good drawing} of a graph $G$ is a drawing where the edges are
non-self-intersecting and each two edges have at most one point in common,
which is either a common end vertex or a crossing. The {\it crossing number} of
a graph $G$ is the minimum number of pairwise intersections of edges in a good
drawing of $G$ in the plane. The {\it $n$-dimensional augmented cube} $AQ_n$,
proposed by S.A. Choudum and V. Sunitha, is an important interconnection
network with good topological properties and applications. In this paper, we
obtain an upper bound on the crossing number of $AQ_n$ less than
$26/324^{n}-(2n^2+7/2n-6)2^{n-2}$.
