  The Wong-Rosay theorem characterizes the strongly pseudoconvex domains of
$\mathbb{C}^n$ by their automorphism groups. It has a lot of generalizations to
other kinds of domains (for example, the weakly pseudoconvex domains). However,
most of them are for domains of $\mathbb{C}^n$. In this note, we generalize the
Wong-Rosay theorem to the simply-connected complete K\"{a}hler manifold with a
negative sectional curvature. One aim of this note is to exhibit a Wong-Rosay
type theorem of manifolds with holomorphic non-invariant metrics.
