  The masses of $1^{--}$ charmonium and bottomonium hybrids are evaluated in
terms of QCD sum rules. We find that the ground state hybrid in charm sector
lies in $m_{H_c}=4.12\sim 4.79$ GeV, while in bottom sector the hybrid may
situated in $m_{H_b} = 10.24\sim 11.15$ GeV. Since the numerical result on
charmonium hybrid mass is not compatible with the charmonium spectra, including
structures newly observed in experiment, we tempt to conclude that such a
hybrid does not purely exist, but rather as an admixture with other states,
like glueball and regular quarkonium, in experimental observation. However, our
result on bottomonium hybrid coincide with the "exotic structure" recently
observed at BELLE.
