  We assign $X(4500)$ as a D-wave tetraquark state and study the decay of
$X(4500)$ $\to$ $J/\psi \phi$. The mass and the decay constant of $X(4500)$ are
calculated by using the SVZ sum rules. For the decay width of $X(4500)$ $\to$
$J/\psi \phi$, we present the calculation within the framework of both the
three-point sum rules and the light-cone sum rules. The strong coupling $g_{X
J/\psi \phi}$ is obtained by considering the soft-meson approximation when we
use the light-cone sum rules calculation. Both calculations show that the decay
of $X(4500)$ $\to$ $J/\psi\phi$ close to the total width of $X(4500)$ if we
assign $X$(4500) as a D-wave tetraquark. In this paper, only the hidden-charm
decay channel is considered. With these results and those from the open-charm
decay channel, we are able to give a more rational conclusion when comparing
with the total width of $X(4500)$. In the future, experiments will be more
helpful in determining whether or not this structure of $X(4500)$ is
appropriate.
