  We study the property of $X(4260)$ resonance by re-analyzing all experimental
data available, especially the $e^+e^- \rightarrow
J/\psi\,\pi^+\pi^-,\,\,\,\omega\chi_{c0}$ cross section data. The final state
interactions of the $\pi\pi$, $K\bar K$ couple channel system are also taken
into account. A sizable coupling between the $X(4260)$ and $\omega\chi_{c0}$ is
found. The inclusion of the $\omega\chi_{c0}$ data indicates a small value of
$\Gamma_{e^+e^-}=23.30\pm 3.55$eV.
