  Basing on the observation of a new $J^{PC}=0^{-+}$ state, $X(2500)$, in the
partial wave analysis of the decay $J/\psi\rightarrow\gamma X\rightarrow
\gamma\phi\phi$ performed by the BESIII Collaboration, we have evaluated the
strong decays of the $X(2500)$ as the $4^1S_0$ and $5^1S_0$ $s\bar{s}$ states
in the $^3P_0$ meson decay model. The predicted total decay width for the
$4^1S_0$ $s\bar{s}$ is about 894.5 MeV, and the one for the $5^1S_0$ $s\bar{s}$
is about 271.1 MeV, which is in agreement with the experimental data
$\Gamma_{X(2500)}=230^{+64+56}_{-35-33}$ MeV. By considering the mass and the
total strong decay width of the $X(2500)$, we propose that the $X(2500)$ state
can be interpreted as a candidate of the $5^1S_0$ $s\bar{s}$ state.
