  Inspired by the newly observed state $X^{*}(3860)$, we analyze the strong
decay behaviors of some charmonium-like states $X^{*}(3860)$,$X(3872)$,
$X(3915)$, $X(3930)$ and $X(3940)$ by the $^{3}P_{0}$ model. We carry out our
work based on the hypothesis that these states are all being the charmonium
systems. Our analysis indicates that $0^{++}$ charmonium state can be a good
candidate for $X^{*}(3860)$ and $1^{++}$ state is the possible assignment for
$X(3872)$. Considering as the $3^{1}S_{0}$ state, the decay behavior of
$X(3940)$ is inconsistent with the experimental data. So, we can not assign
$X(3940)$ as the $3^{1}S_{0}$ charmonium state by present work. Besides, our
analysis imply that it is reasonable to assign $X(3915)$ and $X(3930)$ to be
the same state, $2^{++}$. However, combining our analysis with that of
Zhou~\cite{ZhouZY}, we speculate that $X(3915)$/$X(3930)$ might not be a pure
$c\overline{c}$ systems.
