  We study the possible charmonium-like states with $J^{PC}=0^{--}, 0^{-+}$
using the tetraquark interpolating currents with the QCD sum rules approach.
The extracted masses are around 4.5 GeV for the $0^{--}$ charmonium-like states
and 4.6 GeV for the $0^{-+}$ charmonium-like states while their
bottomonium-like analogues lie around 10.6 GeV. We also discuss the possible
decay, production and the experiment search of the $0^{--}$ charmonium-like
state.
