  We propose a novel type of interpolating field operators, which manifests the
hybrid-like configuration that the charm quark-antiquark pair recoils against
gluonic degrees of freedom. A heavy vector charmonium-like state with a mass of
$4.33(2)\,{\rm GeV}$ is disentangled from the conventional charmonium states in
the quenched approximation. This state has affinity for the hybrid-like
operators but couples less to the relevant quark bilinear operator. We also try
to extract its leptonic decay constant and give a tentative upper limit that it
is less than one tenth of that of $J/\psi$, which corresponds to a leptonic
decay width about dozens of eV. The connection of this state with $X(4260)$ is
also discussed.
